# How do you solve for x in 9=2^(.84x)?

Dec 5, 2015

$x \approx 3.77$ to 2 decimal places

#### Explanation:

Suppose we had $\log \left({x}^{3}\right)$

This is $\log \left(x \times x \times x\right)$

Which is $\log \left(x\right) + \log \left(x\right) + \log \left(x\right)$

Which is $3 \log \left(x\right)$
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Given: $9 = {2}^{0.84 x}$

Take logs of both sides

$\log \left(9\right) = 0.84 x \log \left(2\right)$

$x = \frac{\log \left(9\right)}{0.84 \times \log \left(2\right)}$

$x \approx 3.77$ to 2 decimal places