Question

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

Answer 1

`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`.