Yitzhak S. | Johns Hopkins Engineer, Specializing in Math and Science.Johns Hopkins Engineer, Specializing in ...

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With any question in this form, we always first completely isolate the 'log' part of the function, and then solve from there. To get the log_{8}(2x+7) alone, we solve for it just as we would solve for any other variable.

3log_{8}(2x+7)+8=10

-8 -8

3log_{8}(2x+7) = 2

/3 /3

log_{8}(2x+7) =2/3

Here we need to remove the log term. We know that log_{b}(x) = n is the same thing as saying b^{n }= x. So, we raise 8 to the power of both sides. This gets rid of the log_{8 }term. So:

2x + 7 = 8^{2/3}

2x+7 = 4 and from here we can solve like any other equation