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What is the value of x if e^3x+6 = 8?

What is the value of x if e^3x+6 = 8?-example-1

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We can write any number n in the form
e^(\ln(n)), since
e^x and
\ln(x) are inverse functions, so that


e^(3x+6) = 8 \iff e^(3x+6) = e^(\ln(8))

The bases are the same on both sides, so the exponents must be equal.


3x + 6 = \ln(8)

Solve for x :


3x = \ln(8) - 6


x = \boxed{\frac{\ln(8) - 6}3}

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