Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. log 4 (x over 2) = 2

Question

asked Feb 10, 2021 180k views

1 Answer

Rajim · Answer 1 · 2021-02-15T13:38:03+0000

Answer:

The solution is x = 32.

Explanation:

To solve the logarithmic equation
$\log _4\left((x)/(2)\right)=2$ you must:

Use the logarithmic definition
$\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c$ .

$\log _4\left((x)/(2)\right)=2\quad \Rightarrow \quad (x)/(2)=4^2$

Multiply both sides by 2

$(x)/(2)\cdot \:2=4^2\cdot \:2$

Simplify

x=32