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3 Answers

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 log8(2x+7) alone, we solve for it just as we would solve for any other variable.

3log8(2x+7)+8=10

                 -8   -8

3log8(2x+7)      = 2

       /3              /3

log8(2x+7)        =2/3   

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

2x + 7  = 82/3

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

     -7      -7

2x        = -3

 /2           /2 

x          = -3/2

The generic form of a log and exponent form can be written:

logbx = n      which also mean that       bn = x

Start by getting the equation into the format of logbx = n

1.) Subtract 8 from both sides:     3log8(2x+7) = 2

2.) Divide both sides by 3:           log8(2x+7) = 2/3

3.) Use the relationship between logs and exponents to rewrite the equation without the log

bn = x; where b = 8, x = (2x + 7), and n = 2/3

8(2/3) = 2x + 7

4.) Solve for x

4 = 2x + 7

-3 = 2x

-3/2 = x

So your solution is x = -3/2

Hope this will help you with this problem type in the future!

Isolate log8(2x+7) first,

log8(2x+7) = (10-8)/3 = 2/3

Change to exponential form,

2x+7 = 8^(2/3) = 4

Solve for x,

x = (4-7)/2 = -3/2 <==Answer