Question

what is the value of n if 364500=500000(1-10÷100)^n

Answer 1

Let's solve your equation step-by-step.

364500=500000(1−10/100)n

364500=500000(9/10)n

Step 1: Flip the equation.

500000(9/10)n = 364500

Step 2: Divide both sides by 500000.

$\frac{500000(9/10)n}{500000}$ = $\frac{364500}{500000}$ 

(9/10)n=729/1000

Step 3: Solve Exponent.

(9/10)n=729/1000

log((9/10)n)=log(729/1000)(Take log of both sides)

n*(log(9/10))=log(729/1000)

n=log(729/1000)log(9/10)

n=3
Simplify 

n=3

Answer 2

$364500 = 500000(1- \frac{10}{100} )^n$
$\frac{364500}{500000} = (\frac{100-10}{100} )^n$
$\frac{729}{1000} = ( \frac{9}{10})^n$
$( \frac{9}{10}) ^3=( \frac{9}{10} )^n$
$3 = n$