What is the answer to solvefor m,144=((2^m))/((3^n)) ?

The answer to solvefor m,144=((2^m))/((3^n)) is m=(4ln(2)+ln(3)(n+2))/(ln(2))

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solvefor m,144=((2^m))/((3^n))

solve for

m, 144 = \frac{( 2 ^{m} )}{( 3 ^{n} )}

m = \frac{4 ln ( 2 ) + ln ( 3 ) ( n + 2 )}{ln ( 2 )}

Solution steps

144 = \frac{( 2 ^{m} )}{( 3 ^{n} )}

Apply exponent rules

m ln (2) = ln (16 \cdot 3^{2 + n})

Solve

m ln (2) = ln (16 \cdot 3^{2 + n}) : m = \frac{4 ln ( 2 ) + ln ( 3 ) ( n + 2 )}{ln ( 2 )}

m = \frac{4 ln ( 2 ) + ln ( 3 ) ( n + 2 )}{ln ( 2 )}

\frac{x}{( \frac{1}{2} )} = 2^{x} + 3

(\frac{2}{5})^{3 x - 7} = (\frac{5}{2})^{7 x - 3}

e^{x} + e^{- x} = 2

2^{n - 1} + 2^{n + 1} = 320

3^{3 x - 1} = 2^{x + 3}

What is the answer to solvefor m,144=((2^m))/((3^n)) ?
The answer to solvefor m,144=((2^m))/((3^n)) is m=(4ln(2)+ln(3)(n+2))/(ln(2))