Question

What is the solution of the equation 2 + 3^x = 7? Round your answer to the nearest ten-thousandth.

0.2218

1.4650

0.6826

0.4522

Answer 1

Subtract 2 and take logarithms. Solve the resulting linear equation.
3^x = 5
x*log(3) = log(5)
x = log(5)/log(3)
x ≈ 1.4650

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You know this is the correct choice before you take logs, because you know that 3 has to be raised to a power greater than 1 in order to get a value of 5. The second choice (1.4650) is the only choice greater than 1.