What is 40log_{8}(23)log_{529}(8) ?

The solution to 40log_{8}(23)log_{529}(8) is 20

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simplify 40log_{8}(23)log_{529}(8)

simplify

40 lo g_{8} (23) lo g_{529} (8)

20

Solution steps

40 lo g_{8} (23) lo g_{529} (8)

Apply log rule:

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

lo g_{8} (23) = \frac{ln ( 23 )}{ln ( 8 )}

= 40 \cdot \frac{ln ( 23 )}{ln ( 8 )} lo g_{529} (8)

Apply log rule:

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

lo g_{529} (8) = \frac{ln ( 8 )}{ln ( 529 )}

= 40 \cdot \frac{ln ( 23 )}{ln ( 8 )} \cdot \frac{ln ( 8 )}{ln ( 529 )}

Cross-cancel common factor:

ln (8)

= 40 \cdot \frac{ln ( 23 )}{ln ( 529 )}

ln (529) = 2 ln (23)

= 40 \cdot \frac{ln ( 23 )}{2 ln ( 23 )}

Cancel the common factor:

ln (23)

= 40 \cdot \frac{1}{2}

40 \cdot \frac{1}{2} = 20

= 20

\frac{45}{75}

(- 14)^{2}

(- 3 x - 5) (- x^{2} + x - 5)

\frac{6 z}{2 ( z ^{2} ) ^{5}}

cos^{2} (x) + cos^{2} (x)

What is 40log_{8}(23)log_{529}(8) ?
The solution to 40log_{8}(23)log_{529}(8) is 20