Question 1005203
start with 4^(2x+3) = 5^(x - 2)


take the log of both sides of the equation to get:


log(4^(2x+3)) = log(5^(x-2))


since log(a^b) = b*log(a), apply this property to your expression to get:


(2x+3) * log(4) = (x-2) * log(5)


use the distributive law of multiplication to get:


2x * log(4) + 3 * log(4) = x * log(5) - 2 * log(5)


subtract x * log(5) from both sides of the equation and subtract 3 * log(4) from both sides of the equation to get:


2x * log(4) - x * log(5) = - 2 * log(5) - 3 * log(4)


factor out the x on the left side of the equation to get:


x * (2 * log(4) - log(5)) = -2 * log(5) - 3 * log(4)


divide both sides of the equation by (2 * log(4) - log(5)) to get:


x = (-2 * log(5) - 3 * log(4)) / (2 * log(4) - log(5))


use your calculator to evaluate the expression on the right side of the equation.


you will get x = -6.342908285


replace x in your original equation with that value and you will get:


4^(2x+3) = 5^(x - 2) becomes 4^(2 * -6.342908285 + 3) = 5^(-6.342908285 - 2)


perform the evaluation and you will get:


1.474203235 * 10^-6 = 1.474203235 * 10^-6.


since they're equal, the value for x is good.