Question

How do you solve the equation `log_x 243=5`?

Answer 1

`x=3`

Explanation:

question given
solve `\log_(x)(243)=5`

concept applied
log to exponential conversion `y=x^b\leftrightarrowb=\log_{x}(y)`

• the equation is in the form of `\color(red)(x=log_{b}(y))`

calculation
let's convert to `\color(green)(y)=x^\color(blue)(b)` form.

• in the equation you are given, `\color(blue)(b=5)`, `\color(green)(y=243)`, and you need to find the value for `x`.
• putting this into the equation:
  `\color(green)(243)=x^\color(blue)(5)`
• after this you would either find the fifth root of 243, or you can use a calculator to plug in values.
• answer: x=3

source links
VirtualNerd (concept discussion)
Symbolab (step-by-step)