Question

What is the exact value of 4(10)^5x = 200

Answer 1

For this case we must find the value of the variable "x" of the following expression:

$4(10^{5x})=200$

We divide both sides of the equation by 4:

$10 ^ {5x} = \frac {200} {4}\\10 ^ {5x} = 50$

We find ln on both sides of the equation to remove the exponent variable:

$ln (10^{5x}) = ln (50)\\5x * ln (10) = ln (50)$

We divide both sides of the equation between 5 * ln (10):$x = \frac {ln (50)} {5 * ln (10)}$

In decimal form we have:

$x = 0.33979400$

ANswer:

$x = 0.33979400$