What is (ln(7)-5ln(5))/(ln(5)) ?

The solution to (ln(7)-5ln(5))/(ln(5)) is (ln(7/3125))/(ln(5))

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simplify (ln(7)-5ln(5))/(ln(5))

simplify

\frac{ln ( 7 ) - 5 ln ( 5 )}{ln ( 5 )}

\frac{ln ( \frac{7}{3125} )}{ln ( 5 )}

Solution steps

\frac{ln ( 7 ) - 5 ln ( 5 )}{ln ( 5 )}

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 ln (5) = ln (5^{5})

= \frac{ln ( 7 ) - ln ( 5 ^{5} )}{ln ( 5 )}

Apply log rule:

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

ln (7) - ln (5^{5}) = ln (\frac{7}{5 ^{5}})

= \frac{ln ( \frac{7}{5 ^{5}} )}{ln ( 5 )}

5^{5} = 3125

= \frac{ln ( \frac{7}{3125} )}{ln ( 5 )}

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What is (ln(7)-5ln(5))/(ln(5)) ?
The solution to (ln(7)-5ln(5))/(ln(5)) is (ln(7/3125))/(ln(5))