What is (ln(5))/(ln(5)-2ln(3)) ?

The solution to (ln(5))/(ln(5)-2ln(3)) is (ln(5))/(ln(5/9))

Popular >

simplify (ln(5))/(ln(5)-2ln(3))

simplify

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

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

Decimal Notation

- 2.73813 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} = 9

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

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

lo g_{2} (x + 6) + lo g_{2} (x)

3 lo g_{10} (x) - 6 lo g_{10} (y)

ln (11) + 6 ln (x) + 6 ln (y)

lo g_{10} (x - 2) + lo g_{10} (x + 1)

What is (ln(5))/(ln(5)-2ln(3)) ?
The solution to (ln(5))/(ln(5)-2ln(3)) is (ln(5))/(ln(5/9))