SOLUTION: Solve for x: {{{5*6^(2x-3)+1=8}}}

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Question 130626: Solve for x: 5%2A6%5E%282x-3%29%2B1=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2A6%5E%282x-3%29%2B1=8 Start with the given equation


5%2A6%5E%282x-3%29=7 Subtract 1 from both sides


6%5E%282x-3%29=7%2F5 Divide both sides by 5


log%2810%2C%286%5E%282x-3%29%29%29=log%2810%2C%287%2F5%29%29 Take the log of both sides


%282x-3%29log%2810%2C%286%29%29=log%2810%2C%287%2F5%29%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


2x-3=log%2810%2C%287%2F5%29%29%2Flog%2810%2C%286%29%29 Divide both sides by log%2810%2C%286%29%29


2x-3=log%286%2C%287%2F5%29%29 Now use the change of base formula to simplify log%2810%2C%287%2F5%29%29%2Flog%2810%2C%286%29%29 to get log%286%2C%287%2F5%29%29


2x=log%286%2C%287%2F5%29%29%2B3 Add 3 to both sides



x=%28log%286%2C%287%2F5%29%29%2B3%29%2F2 Divide both sides by 2 to isolate x