Question

HELP!

What is the solution to the equation below? Round your answer to two decimal places. 4x = 20

A. x = 2.99
B. x = 0.46
C. x = 1.30
D. x = 2.16

Answer 1

Answer: D. x = 2.16

Explanation:

The given equation is
`4^x= 20`

Taking log on both sides, we get

`\log 4^x =\log 20`

Using properties of logarithm

`\log a^b=b\loga`

We have,

`x\log 4= \log 20\\\\\Rightarrow\ x=(\log 20)/(\log 4)\\\\\Rightarrow\ x=\log (1.3010)/(0.6021) \\\\\Rightarrow\ x= 2.1608\approx 2.16`

Hence, the solution to the given equation is x = 2.16.

So the correct option is D.