What is join (5ln(9/74))/(ln(59/74)) ?

The solution to join (5ln(9/74))/(ln(59/74)) is (ln(\frac{59049)/(74^5))}{ln(59/74)}

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join (5ln(9/74))/(ln(59/74))

join

\frac{5 ln ( \frac{9}{74} )}{ln ( \frac{59}{74} )}

\frac{ln ( \frac{59049}{7 4 ^{5}} )}{ln ( \frac{59}{74} )}

Decimal Notation

46.50294 \dots

Solution steps

\frac{5 ln ( \frac{9}{74} )}{ln ( \frac{59}{74} )}

Apply log rule:

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

5 ln (\frac{9}{74}) = ln ((\frac{9}{74})^{5})

= \frac{ln ( ( \frac{9}{74} ) ^{5} )}{ln ( \frac{59}{74} )}

(\frac{9}{74})^{5} = \frac{9 ^{5}}{7 4 ^{5}}

= \frac{ln ( \frac{9 ^{5}}{7 4 ^{5}} )}{ln ( \frac{59}{74} )}

9^{5} = 59049

= \frac{ln ( \frac{59049}{7 4 ^{5}} )}{ln ( \frac{59}{74} )}

- lo g_{10} (1.6 \cdot 1 0^{- 3})

- 2 ln (\frac{2}{2})

lo g_{10} (\frac{100}{x \cdot y ^{4}})

4 lo g_{10} (x) + lo g_{10} (y)

ln (4 x^{2} - 3) - ln (x^{2})

What is join (5ln(9/74))/(ln(59/74)) ?
The solution to join (5ln(9/74))/(ln(59/74)) is (ln(\frac{59049)/(74^5))}{ln(59/74)}