What is join (4ln(2))/(ln(512/3)) ?

The solution to join (4ln(2))/(ln(512/3)) is (ln(16))/(ln(512/3))

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join (4ln(2))/(ln(512/3))

join

\frac{4 ln ( 2 )}{ln ( \frac{512}{3} )}

\frac{ln ( 16 )}{ln ( \frac{512}{3} )}

Decimal Notation

0.53944 \dots

Solution steps

\frac{4 ln ( 2 )}{ln ( \frac{512}{3} )}

Apply log rule:

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

4 ln (2) = ln (2^{4})

= \frac{ln ( 2 ^{4} )}{ln ( \frac{512}{3} )}

2^{4} = 16

= \frac{ln ( 16 )}{ln ( \frac{512}{3} )}

ln (\frac{400}{100})

ln (\frac{4421}{28350})

- lo g_{10} (4.6 \cdot 1 0^{- 7})

ln (\frac{1}{1 + x ^{2}})

3 lo g_{10} (x) - lo g_{10} (2)

What is join (4ln(2))/(ln(512/3)) ?
The solution to join (4ln(2))/(ln(512/3)) is (ln(16))/(ln(512/3))