diff --git a/clippy_lints/src/floating_point_arithmetic.rs b/clippy_lints/src/floating_point_arithmetic.rs
index 46a2396fcd12..8d580c714885 100644
--- a/clippy_lints/src/floating_point_arithmetic.rs
+++ b/clippy_lints/src/floating_point_arithmetic.rs
@@ -234,6 +234,38 @@ fn check_expm1(cx: &LateContext<'_, '_>, expr: &Expr) {
     }
 }
 
+// Expressions are considered equivalent if they are constant and evaluate to the
+// same value or if they refer to the same variable.
+fn are_exprs_equivalent(cx: &LateContext<'_, '_>, left: &Expr, right: &Expr) -> bool {
+    // Checks whether the values are constant and equal
+    if_chain! {
+        if let Some((left_value, _)) = constant(cx, cx.tables, left);
+        if let Some((right_value, _)) = constant(cx, cx.tables, right);
+        if left_value == right_value;
+        then {
+            return true;
+        }
+    }
+
+    // Checks whether the values are the same variable
+    if_chain! {
+        if let ExprKind::Path(ref left_qpath) = left.kind;
+        if let QPath::Resolved(_, ref left_path) = *left_qpath;
+        if left_path.segments.len() == 1;
+        if let def::Res::Local(left_local_id) = qpath_res(cx, left_qpath, left.hir_id);
+        if let ExprKind::Path(ref right_qpath) = right.kind;
+        if let QPath::Resolved(_, ref right_path) = *right_qpath;
+        if right_path.segments.len() == 1;
+        if let def::Res::Local(right_local_id) = qpath_res(cx, right_qpath, right.hir_id);
+        if left_local_id == right_local_id;
+        then {
+            return true;
+        }
+    }
+
+    false
+}
+
 fn check_log_division(cx: &LateContext<'_, '_>, expr: &Expr) {
     let log_methods = ["log", "log2", "log10", "ln"];
 
@@ -250,32 +282,9 @@ fn check_log_division(cx: &LateContext<'_, '_>, expr: &Expr) {
             let left_recv = &left_args[0];
             let right_recv = &right_args[0];
 
-            if left_method == "log" {
-                if_chain! {
-                    // Checks whether the bases are constant and equal
-                    if let Some((numerator_base, _)) = constant(cx, cx.tables, &left_args[1]);
-                    if let Some((denominator_base, _)) = constant(cx, cx.tables, &right_args[1]);
-                    if numerator_base == denominator_base;
-                    then { }
-                    else {
-                        if_chain! {
-                            // Checks whether the bases are the same variable
-                            if let ExprKind::Path(ref left_base_qpath) = &left_args[1].kind;
-                            if let QPath::Resolved(_, ref left_base_path) = *left_base_qpath;
-                            if left_base_path.segments.len() == 1;
-                            if let def::Res::Local(left_local_id) = qpath_res(cx, left_base_qpath, expr.hir_id);
-                            if let ExprKind::Path(ref right_base_qpath) = &right_args[1].kind;
-                            if let QPath::Resolved(_, ref right_base_path) = *right_base_qpath;
-                            if right_base_path.segments.len() == 1;
-                            if let def::Res::Local(right_local_id) = qpath_res(cx, right_base_qpath, expr.hir_id);
-                            if left_local_id == right_local_id;
-                            then { }
-                            else {
-                                return;
-                            }
-                        }
-                    }
-                }
+            // Return early when bases are not equal
+            if left_method == "log" && !are_exprs_equivalent(cx, &left_args[1], &right_args[1]) {
+                return;
             }
 
             // Reduce the expression further for bases 2, 10 and e
@@ -293,7 +302,7 @@ fn check_log_division(cx: &LateContext<'_, '_>, expr: &Expr) {
                 cx,
                 FLOATING_POINT_IMPROVEMENTS,
                 expr.span,
-                "x.log(b) / y.log(b) can be expressed more succinctly",
+                "x.log(b) / y.log(b) can be reduced to x.log(y)",
                 "consider using",
                 suggestion,
                 Applicability::MachineApplicable,
diff --git a/tests/ui/floating_point_arithmetic.stderr b/tests/ui/floating_point_arithmetic.stderr
index 249bd559be63..076b8d4fefe6 100644
--- a/tests/ui/floating_point_arithmetic.stderr
+++ b/tests/ui/floating_point_arithmetic.stderr
@@ -192,73 +192,73 @@ error: (e.pow(x) - 1) can be computed more accurately
 LL |     let _ = x.exp() - 1.0 + 2.0;
    |             ^^^^^^^^^^^^^ help: consider using: `x.exp_m1()`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:90:13
    |
 LL |     let _ = x.log2() / y.log2();
    |             ^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:91:13
    |
 LL |     let _ = x.log10() / y.log10();
    |             ^^^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:92:13
    |
 LL |     let _ = x.ln() / y.ln();
    |             ^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:93:13
    |
 LL |     let _ = x.log(4.0) / y.log(4.0);
    |             ^^^^^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:94:13
    |
 LL |     let _ = x.log(b) / y.log(b);
    |             ^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:96:13
    |
 LL |     let _ = x.log(b) / 2f32.log(b);
    |             ^^^^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log2()`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:102:13
    |
 LL |     let _ = x.log2() / y.log2();
    |             ^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:103:13
    |
 LL |     let _ = x.log10() / y.log10();
    |             ^^^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:104:13
    |
 LL |     let _ = x.ln() / y.ln();
    |             ^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:105:13
    |
 LL |     let _ = x.log(4.0) / y.log(4.0);
    |             ^^^^^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:106:13
    |
 LL |     let _ = x.log(b) / y.log(b);
    |             ^^^^^^^^^^^^^^^^^^^ help: consider using: `x.log(y)`
 
-error: x.log(b) / y.log(b) can be expressed more succinctly
+error: x.log(b) / y.log(b) can be reduced to x.log(y)
   --> $DIR/floating_point_arithmetic.rs:108:13
    |
 LL |     let _ = x.log(b) / 2f64.log(b);