What is log_{7}(a)*log_{b}(7) ?

The solution to log_{7}(a)*log_{b}(7) is log_{b}(a)

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simplify log_{7}(a)*log_{b}(7)

simplify

lo g_{7} (a) \cdot lo g_{b} (7)

lo g_{b} (a)

Solution steps

lo g_{7} (a) lo g_{b} (7)

Apply log rule:

lo g_{a} (b) = \frac{lo g _{c} ( b )}{lo g _{c} ( a )}

lo g_{7} (a) = \frac{ln ( a )}{ln ( 7 )}

= \frac{ln ( a )}{ln ( 7 )} lo g_{b} (7)

Apply log rule:

lo g_{a} (b) = \frac{lo g _{c} ( b )}{lo g _{c} ( a )}

lo g_{b} (7) = \frac{ln ( 7 )}{ln ( b )}

= \frac{ln ( a )}{ln ( 7 )} \cdot \frac{ln ( 7 )}{ln ( b )}

Cross-cancel common factor:

ln (7)

= \frac{ln ( a )}{ln ( b )}

Apply log rule:

\frac{lo g _{c} ( b )}{lo g _{c} ( a )} = lo g_{a} (b)

\frac{ln ( a )}{ln ( b )} = lo g_{b} (a)

= lo g_{b} (a)

(x - 2) (2 x + 5) = 2 x + 5

(x - 5)^{2} = 81

- 4 (3^{2} - 8) + 1

y - 3 < 5 y + 1

∣ u ∣ = 0

What is log_{7}(a)*log_{b}(7) ?
The solution to log_{7}(a)*log_{b}(7) is log_{b}(a)