What is the answer to solvefor a,3^a*(6)^b=2^5 ?

The answer to solvefor a,3^a*(6)^b=2^5 is a=(ln(\frac{2^{5-b})/(3^b))}{ln(3)}

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solvefor a,3^a*(6)^b=2^5

solve for

a, 3^{a} \cdot (6)^{b} = 2^{5}

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

Solution steps

3^{a} (6)^{b} = 2^{5}

Divide both sides by

6^{b}

3^{a} = \frac{2 ^{5}}{6 ^{b}}

Simplify

\frac{2 ^{5}}{6 ^{b}} : \frac{2 ^{5 - b}}{3 ^{b}}

3^{a} = \frac{2 ^{5 - b}}{3 ^{b}}

Apply exponent rules

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

Solve

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

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

1.41 = 2^{x}

(\frac{8}{9})^{3} \cdot (\frac{8}{9})^{- 6} = (\frac{8}{9})^{2 x - 1}

3^{2 x - 2} = 81

- (\frac{5}{4}) = (\frac{- 4}{5})^{x}

2^{2} x + 3 + 7 = 15. 2^{x}

What is the answer to solvefor a,3^a*(6)^b=2^5 ?
The answer to solvefor a,3^a*(6)^b=2^5 is a=(ln(\frac{2^{5-b})/(3^b))}{ln(3)}