SOLUTION: Solve for x: {{{2log(7,(x))=2+log(7,(16))}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve for x: {{{2log(7,(x))=2+log(7,(16))}}}      Log On


   

Question 130682: Solve for x:

2log%287%2C%28x%29%29=2%2Blog%287%2C%2816%29%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2log%287%2C%28x%29%29=2%2Blog%287%2C%2816%29%29 Start with the given equation.


log%287%2C%28x%5E2%29%29=2%2Blog%287%2C%2816%29%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


log%287%2C%28x%5E2%29%29-log%287%2C%2816%29%29=2 Subtract log%287%2C%2816%29%29 from both sides


log%287%2C%28x%5E2%2F16%29%29=2 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29



7%5E2=x%5E2%2F16 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


49=x%5E2%2F16 Evaluate 7%5E2 to get 49


784=x%5E2 Multiply both sides by 16


sqrt%28784%29=x Take the square root of both sides


28=x Take the square root of 784 to get 28



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Answer:

So the solution is x=28