Given that
{2}^{2x + 2} \times {5}^{x - 1} = {8}^{x} \times {5}^{2x}22x+2×5x−1=8x×52x
evaluate
{10}^{x}10x

Answer:

   



   

make everything simpler for us before we use logarithms. 

can be rewritten as 

   

divide both sides by   

   

divide both sides by 

   

use exponent law:  

   

take the logarithm base-10 of both sides of the equation

   

use log law:  

   

distribute the logs (they are just numbers)

   

isolate all the x-terms together; move everything else away.
here, we move x terms to the right and everything else to the left

   

factor out x from right side

   

divide both sides by log(5) + log(2)

   

for the coefficient of 2, use log law 

   

in numerator, use log law: log(x) - log(y) = log(x/y)
in denominator, use log law: log(x) + log(y) = log(x  · y)

   

multiply both sides by log(10)

   

use log law for coefficient of x

   

drop the logs