# 3log10-log(x+2) = 2 x=8?

## The teacher says it = 8 But doesnt provide work Can anyone help me?

May 22, 2018

$3 \log 10 - \log \left(x + 2\right) = 2$

We can begin by evaluating the logarithmic value.

$3 \left(1\right) - \log \left(x + 2\right) = 2$

$3 - \log \left(x + 2\right) = 2$

We then need to isolate the variable.

$\log \left(x + 2\right) = 1$

Next, we simplify the logarithm by converting it to exponent form.

${\log}_{b} x = y$ becomes ${b}^{y} = x$

In this case, $b = 10$, the standard base for logarithms if not stated otherwise. Also, $x = x + 2$ and $y = 1$.

$\log \left(x + 2\right) = 1$ becomes ${10}^{1} = x + 2$

$10 = x + 2$

$8 = x$

We can check the answer $x = 8$ and plug this value into the equation.

$3 \log 10 - \log \left(8 + 2\right) = 2$

$3 \log 10 - \log 10 = 2$

$2 \log 10 = 2$

To isolate the logarithm, we need to further simplify.

$\frac{\cancel{2} \log 10}{\cancel{2}} = \frac{\cancel{2}}{\cancel{2}}$

$\log 10 = 1$

$1 = 1$

Therefore, $x = 8$ works.