Question

Question 29 of 40Solve for x. 4-25× = 21.OA. 0.48OB. 0.31OC. 0.42OD. 0.08NOUSSA

Answer 1

`A.\text{ }0.48`

Step-by-step explanation

We want to solve for x in the equation:

`4*2^(5x)=21`

First, divide both sides of the equation by 4:

`\begin{gathered} (4*2^(5x))/(4)=(21)/(4) \\ \\ 2^(5x)=5.25 \end{gathered}`

Find the logarithm of both sides of the equation:

`\log2^(5x)=\log5.25`

Simplify the left-hand side of the equation:

`5x(\log2)=\log5.25`

Divide both sides by log2:

`5x=(\log5.25)/(\log2)=2.392`

Divide both sides of the equation by 5:

`\begin{gathered} (5x)/(5)=(2.392)/(5) \\ \\ x=0.48 \end{gathered}`

The answer is option A.