What is log_{25}(10)*log_{10}(125) ?

The solution to log_{25}(10)*log_{10}(125) is 3/2

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simplify log_{25}(10)*log_{10}(125)

simplify

lo g_{25} (10) \cdot lo g_{10} (125)

\frac{3}{2}

Solution steps

lo g_{25} (10) lo g_{10} (125)

Apply log rule:

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

lo g_{25} (10) = \frac{ln ( 10 )}{ln ( 25 )}

= \frac{ln ( 10 )}{ln ( 25 )} lo g_{10} (125)

Apply log rule:

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

lo g_{10} (125) = \frac{ln ( 125 )}{ln ( 10 )}

= \frac{ln ( 10 )}{ln ( 25 )} \cdot \frac{ln ( 125 )}{ln ( 10 )}

Cross-cancel common factor:

ln (10)

= \frac{ln ( 125 )}{ln ( 25 )}

ln (125) = 3 ln (5)

ln (25) = 2 ln (5)

= \frac{3 ln ( 5 )}{2 ln ( 5 )}

Cancel the common factor:

ln (5)

= \frac{3}{2}

1 0^{- 6.5}

(2 m - n)^{3}

\frac{1}{4} \times 8

(- 6 w)^{3}

3 \frac{1}{5} x + 10 \frac{7}{9} - 2 \frac{2}{5} x - 10 \frac{8}{9}

What is log_{25}(10)*log_{10}(125) ?
The solution to log_{25}(10)*log_{10}(125) is 3/2