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

Option D is correct.

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.