How do you solve #4^x = 7^(x-4)#?
1 Answer
Dec 4, 2015
Explanation:
Given the exponential equation
To solve exponential equation we can use logarithm.
Step 1: Take log of both side
Using the power rule of logarithm
# x log 4 = (x-4) log 7#
Then distribute
# x log 4 = x log 7 - 4 log 7#
Then bring all the "x" on one side
#x log 4 - x log 7 = -4 log 7#
Factor out the greatest common factor
#x(log 4 - log 7) = -4 log 7#
Isolate "x"
# x = (-4log 7)/(log 4 - log 7)#
#x~= -6.7745#