What is the answer to sqrt(3)^{3x+4}=6^{x-5} ?

The answer to sqrt(3)^{3x+4}=6^{x-5} is x=(10ln(6)+4ln(3))/(ln(4/3))

Solve for x: sqrt(3)^{3x+4}=6^{x-5}

The solution is x=(10ln(6)+4ln(3))/(ln(4/3))

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3^{3 x + 4} = 6^{x - 5}

x = \frac{10 ln ( 6 ) + 4 ln ( 3 )}{ln ( \frac{4}{3} )}

Decimal Notation

x = 77.55799 \dots

Solution steps

(3)^{3 x + 4} = 6^{x - 5}

Apply exponent rules

\frac{1}{2} (3 x + 4) ln (3) = (x - 5) ln (6)

Solve

\frac{1}{2} (3 x + 4) ln (3) = (x - 5) ln (6) : x = \frac{10 ln ( 6 ) + 4 ln ( 3 )}{ln ( \frac{4}{3} )}

x = \frac{10 ln ( 6 ) + 4 ln ( 3 )}{ln ( \frac{4}{3} )}

4 e^{2 x} + x - 4 = 0

3^{x - 1} = \frac{1}{3}

- x e^{- x} + 9 e^{- x} = 0

e^{- 36 x} - e^{- 39 x} = 0.025 e^{- 33 x}

9 \times e^{2 z} = 54

What is the answer to sqrt(3)^{3x+4}=6^{x-5} ?
The answer to sqrt(3)^{3x+4}=6^{x-5} is x=(10ln(6)+4ln(3))/(ln(4/3))
Solve for x: sqrt(3)^{3x+4}=6^{x-5}
The solution is x=(10ln(6)+4ln(3))/(ln(4/3))