Question

How do you solve `2^x=64`?

Answer 1

I got `x=6`

Explanation:

We can write it as:
`2^x=2^6`
so that `x=6`

Answer 2

`x=6`

Explanation:

`2^x=64`

Just in case your teacher wants you to solve this the fancy way...

`log2^x=log64color(white)(aaa)`Take the log of both sides

`xlog2=log64color(white)(aaa)`Use the log rule `logx^a=alogx`

`(xlog2)/log2=log64/log2color(white)(aaa)`Divide both sides by log2

`x=6`

Or, if you're not allowed to use a calculator...

`log_2 2^x=log_2 64`

`xlog_2 2=log_2 64`

`(xlog_2 2)/log_2 2=log_2 64/log_2 2`

`log_color(red)2 color(violet)(64) = color(blue)6` because the answer to a log problem is the exponent `color(blue)6` that will make the base `color(red)2` equal the argument `color(violet)(64)`. In other words, `color(red)2^color(blue)6=color(violet)(64)`. Similarly, `log_color(red)2 color(violet)(2) =color(blue)1` because `color(red)2^color(blue)1=color(violet)2`. But if you knew that, you could solve this problem without all the fancy math!

`x=6/1`

`x=6`