What is (ln(37)+2ln(4))/(ln(4)) ?

The solution to (ln(37)+2ln(4))/(ln(4)) is (ln(592))/(2ln(2))

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simplify (ln(37)+2ln(4))/(ln(4))

simplify

\frac{ln ( 37 ) + 2 ln ( 4 )}{ln ( 4 )}

\frac{ln ( 592 )}{2 ln ( 2 )}

Decimal Notation

4.60472 \dots

Solution steps

\frac{ln ( 37 ) + 2 ln ( 4 )}{ln ( 4 )}

Apply log rule:

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

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

= \frac{ln ( 37 ) + ln ( 4 ^{2} )}{ln ( 4 )}

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (37) + ln (4^{2}) = ln (4^{2} \cdot 37)

= \frac{ln ( 4 ^{2} \cdot 37 )}{ln ( 4 )}

37 \cdot 4^{2} = 592

= \frac{ln ( 592 )}{ln ( 4 )}

Simplify

ln (4) : 2 ln (2)

= \frac{ln ( 592 )}{2 ln ( 2 )}

ln (\frac{e ^{2 x} cos ( 3 x )}{x - 4})

\frac{π}{8} ln (\frac{13}{9})

ln (\frac{tan ( x )}{2})

- lo g_{2} (\frac{1}{6})

2 lo g_{3} (2) - 3 lo g_{3} (4) + 2 lo g_{3} (5)

What is (ln(37)+2ln(4))/(ln(4)) ?
The solution to (ln(37)+2ln(4))/(ln(4)) is (ln(592))/(2ln(2))