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

Question

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

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Answer 1 · 2018-05-22T01:16:47

$3log10-log(x+2)=2$

We can begin by evaluating the logarithmic value.

$3(1)-log(x+2)=2$

$3-log(x+2)=2$

We then need to isolate the variable.

$log(x+2)=1$

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

$log_bx=y$ becomes $b^y=x$

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

$log(x+2)=1$ becomes $10^1=x+2$

$10=x+2$

$8=x$

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

$3log10-log(8+2)=2$

$3log10-log10=2$

$2log10=2$

To isolate the logarithm, we need to further simplify.

$(cancel(2)log10)/cancel(2)=cancel(2)/cancel(2)$

$log10=1$

$1=1$

Therefore, $x=8$ works.