SOLUTION: solve for x -.5log(7)^x=log(7)^.5

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve for x -.5log(7)^x=log(7)^.5      Log On


   

Question 198359: solve for x
-.5log(7)^x=log(7)^.5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-0.5%2Alog%287%2C%28x%29%29=log%287%2C%280.5%29%29 Start with the given equation.


log%287%2C%28x%5E%28-0.5%29%29%29=log%287%2C%280.5%29%29 Rewrite the left side using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


x%5E%28-0.5%29=0.5 Since the bases are equal, this means that the arguments are equal.


1%2Fx%5E%280.5%29=0.5 Rewrite the left side with a positive exponent.


1=0.5x%5E%280.5%29 Multiply both sides by x%5E%280.5%29.


1%2F0.5=x%5E%280.5%29 Divide both sides by 0.5.


2=x%5E%280.5%29 Divide


x%5E%280.5%29=2 Rearrange the equation


sqrt%28x%29=2 Convert to radical form


x=2%5E2 Square both sides


x=4 Square 2 to get 4


So the solution is x=4