How do you solve #3^x-2=11#?

1 Answer
Jim G.
Sep 7, 2016

#x≈2.335#

Explanation:

We use the #color(blue)"law of logarithms"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(logx^n=nlogx)color(white)(a/a)|)))#

#3^x-2=11rArr3^x=13#

Now take the ln of both sides. I have used ln but a log to any base can be used.

#rArrln3^x=ln13#

Using the above law allows us to obtain x as a multiplier.

#xln3=ln13rArrx=(ln13)/(ln3)≈2.335#

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