How do you find the inverse of #y = 1/3log(2x+5) - 4#?

1 Answer
MathMints
Dec 31, 2015

#x=1/2(10^(3(y+4))-5)#

Explanation:

Flip the equation for convenience: #1/3log(2x+5)-4=y#

Isolate the logarithm: #log(2x+5)=3(y+4)#

Use exponents to remove the logarithm: #2x+5=10^(3(y+4))#

Finally, isolate #x#, to give you the inverse function:

#x=1/2(10^(3(y+4))-5)#

Note: This answer assumes that #log(x) = log_10(x)#. If the intended logarithm was intended to be base #e#, then change the #10# in the third step to #e#.

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