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

1 Answer
Nov 25, 2016

Answer:

#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)