How do you find the inverse function $f (x) = 18 + ln (x)$ $f(x) = 18 + ln(x)$ ?

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Answer 1 · 2015-10-22T17:13:45

If memory serves me correctly: $y = e^{x - 18}$ $" "y=e^(x-18)$
I would recommend you check this against another source!

Given that $f (x) = ln (x) + 18$ $f(x)=ln(x) + 18$

Write as $y = ln (x) + 18$ $y=ln(x)+18$

Then $ln (x) = y - 18$ $ln(x)=y-18$

Consider another way of writing $ln (x)$ $ln(x)$

This is in fact $e^{something} = x$ $e^("something") = x$

In this case $something = y - 18$ $"something" = y-18$ giving:

$x = e^{y - 18}$ $x=e^(y-18)$

Now all you have to do is exchange the letters $x and y$ $" "x " and " y$ giving:

$y = e^{x - 18}$ $y=e^(x-18)$

How do you find the inverse function f(x) = 18 + ln(x)f(x)=18+ln(x)f(x) = 18 + ln(x)?