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

Question

asked Nov 27, 2020 186k views

1 Answer

Sevan · Answer 1 · 2020-12-04T05:57:56+0000

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

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