What is (ln(7))/(2ln(3)-ln(7)) ?

The solution to (ln(7))/(2ln(3)-ln(7)) is (ln(7))/(ln(9/7))

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simplify (ln(7))/(2ln(3)-ln(7))

simplify

\frac{ln ( 7 )}{2 ln ( 3 ) - ln ( 7 )}

\frac{ln ( 7 )}{ln ( \frac{9}{7} )}

Decimal Notation

7.74293 \dots

Solution steps

\frac{ln ( 7 )}{2 ln ( 3 ) - ln ( 7 )}

Apply log rule:

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

2 ln (3) = ln (3^{2})

= \frac{ln ( 7 )}{ln ( 3 ^{2} ) - ln ( 7 )}

Apply log rule:

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

ln (3^{2}) - ln (7) = ln (\frac{3 ^{2}}{7})

= \frac{ln ( 7 )}{ln ( \frac{3 ^{2}}{7} )}

3^{2} = 9

= \frac{ln ( 7 )}{ln ( \frac{9}{7} )}

\frac{1}{2} ln (x - 9) + \frac{1}{2} ln (x)

lo g_{14} (\frac{14}{y})

lo g_{10} (\frac{1}{120})

lo g_{10} (\frac{y ^{5}}{x})

\frac{3}{8} \cdot ln (\frac{8}{3})

What is (ln(7))/(2ln(3)-ln(7)) ?
The solution to (ln(7))/(2ln(3)-ln(7)) is (ln(7))/(ln(9/7))