SOLUTION: I need to find the solution set Log 2^(5x+8)=2

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Question 1009517: I need to find the solution set
Log 2^(5x+8)=2
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28+2%5E%285x%2B8%29%29%29=2+........change to base 10
log%28%28+2%5E%285x%2B8%29%29%29%2Flog%28%28+10%29%29=2+
log%28%28+2%5E%285x%2B8%29%29%29=2log%28%28+10%29%29+
log%28%28+2%5E%285x%2B8%29%29%29=+log%28%28+10%5E2%29%29+
log%28%28+2%5E%285x%2B8%29%29%29=+log%28%28+10%2A10%29%29+
log%28%28+2%5E%285x%2B8%29%29%29=+log%28%28+10%29%29%2Blog%28%2810%29%29+
%285x%2B8%29log%28%28+2%29%29=+log%28%28+2%2A5%29%29%2Blog%28%282%2A5%29%29+

%285x%2B8%29log%28%28+2%29%29=+2log%28%28+2%29%29%2B2log%28%285%29%29+
5x%2B8=+2log%28%28+2%29%29%2Flog%28%28+2%29%29%2B2log%28%285%29%29%2Flog%28%28+2%29%29+
5x=+2%2B2log%28%285%29%29%2Flog%28%28+2%29%29+-8
5x=+2log%28%285%29%29%2Flog%28%28+2%29%29+-6
x=+2log%28%285%29%29%2F5log%28%28+2%29%29+-6%2F5
x=+%282%2F5%29%28log%28%285%29%29%2Flog%28%28+2%29%29%29+-6%2F5
x=+%282%2F5%29%28log%28%285%29%29%2Flog%28%28+2%29%29+-3%29


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
I need to find the solution set
Log 2^(5x+8)=2 
log+2%5E%285x+%2B+8%29+=+2

2%5E%285x+%2B+8%29+=+10%5E2 

log+2%5E%285x+%2B+8%29+=+log+10%5E2 -------  Taking LOG of each side

(5x + 8) %22%2A%22 log 2 = 2 %22%2A%22 log 10

(5x + 8) %22%2A%22 log 2 = 2

5x+%2B+8+=+2%2Flog+2

5x + 8 = 6.643856

5x = 6.643856 – 8

5x = - 1.356144

x+=+-+1.356144%2F5, or highlight_green%28-+0.27123%29