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.