Question

What is the solution of the equation 53x = 15? Round your answer to the nearest ten-thousandth.
A .2.4662
B. 0.9542
C. 1.7829
D. 0.5609

Answer 1

53x = 15
x = 15 / 53 = 0.2830188679
Which is not one of the answers.

Answer 2

Answer:

Option D is correct.

Step-by-step explanation:

Given equation is $5^{3x}=15$

we have to find the solution of above equation.

Equation is

$5^{3x}=15$

Taking log on both sides, we get

$log{5^{3x}}=log{15}$

As, $log{a^b}=bloga$

⇒ $log{5^{3x}}=log{15}$

⇒ $3xlog{5}=log{15}$

⇒ $x=\frac{log{15}}{3.log{5}}=0.5608687\sim0.5609$    

Option D is correct.