How do you find the inverse of y = 1/3log(2x+5) - 4y=13log(2x+5)4?

1 Answer
Dec 31, 2015

x=1/2(10^(3(y+4))-5)x=12(103(y+4)5)

Explanation:

Flip the equation for convenience: 1/3log(2x+5)-4=y13log(2x+5)4=y

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

Use exponents to remove the logarithm: 2x+5=10^(3(y+4))2x+5=103(y+4)

Finally, isolate xx, to give you the inverse function:

x=1/2(10^(3(y+4))-5)x=12(103(y+4)5)

Note: This answer assumes that log(x) = log_10(x)log(x)=log10(x). If the intended logarithm was intended to be base ee, then change the 1010 in the third step to ee.