# How do you solve log_x 16 = 4?

Jun 8, 2018

$x = 2$

${\log}_{2} 16 = 4 \text{ "hArr" } {2}^{4} = 16$

#### Explanation:

Log form and index form are interchangeable.

${\log}_{a} b = c \text{ "hArr" } {a}^{c} = b$

${\log}_{x} 16 = 4$ can be read as asking the question....

"What number, when raised to $4 t h$ power will give 16?"

In index form this means: ${x}^{4} = 16$

It really does help to know the first few powers of the numbers up to $10$ by heart.

The powers of $2$ are :

$1 , \text{ "2," "4," "8," "color(blue)(16)," "32," "64," } 128 \ldots .$

This means ${2}^{4} = 16$, which gives us the answer we need.

$x = 2$

Jun 8, 2018

$x = 2$

#### Explanation:

lets say that to put this into exponential form, we can make 4 = y and 16 = the answer.

${x}^{4} = 16$

$x = 2$