What is the answer to (e^{5x})/(e^{-3x+1)}-8=0 ?

The answer to (e^{5x})/(e^{-3x+1)}-8=0 is x=(3ln(2)+1)/8

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(e^{5x})/(e^{-3x+1)}-8=0

\frac{e ^{5 x}}{e ^{- 3 x + 1}} - 8 = 0

x = \frac{3 ln ( 2 ) + 1}{8}

Decimal Notation

x = 0.38493 \dots

Solution steps

\frac{e ^{5 x}}{e ^{- 3 x + 1}} - 8 = 0

Apply exponent rules

e^{8 x - 1} - 8 = 0

Add

8

to both sides

e^{8 x - 1} - 8 + 8 = 0 + 8

Simplify

e^{8 x - 1} = 8

Apply exponent rules

8 x - 1 = ln (8)

Solve

8 x - 1 = ln (8) : x = \frac{3 ln ( 2 ) + 1}{8}

x = \frac{3 ln ( 2 ) + 1}{8}

Verify Solutions:

x = \frac{3 ln ( 2 ) + 1}{8}

True

The solution is

x = \frac{3 ln ( 2 ) + 1}{8}

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What is the answer to (e^{5x})/(e^{-3x+1)}-8=0 ?
The answer to (e^{5x})/(e^{-3x+1)}-8=0 is x=(3ln(2)+1)/8