# How do you solve 1.6= log(4x)?

Nov 25, 2015

I found: $x = 9.9526$ for the log in base $10$.

#### Explanation:

It depends upon the base, $b$, of your log:
$1.6 = {\log}_{b} \left(4 x\right)$
normally $b$ would be $10$ because it can be easily evaluated using a pocket calculator; if your base is different, in the next part, simply use your given value instead of $10$.

Use the definition of log:

${\log}_{b} x = a \to x = {b}^{a}$

so that:
$1.6 = {\log}_{b} \left(4 x\right)$ becomes:
$4 x = {b}^{1.6}$
where, if $b = 10$, then;
$x = \frac{1}{4} \cdot {10}^{1.6}$
$x = 9.9526$