What is the inverse of $y = log (x - 3) ?$ $y=log(x-3)?$ ?

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Answer 1 · 2015-11-01T11:03:22

$y = 10^{x} + 3$ $y=10^x+3$

The inverse of a logarithmic function $y = {log}_{a} x$ $y=log_ax$ is the exponential function $y = a^{x}$ $y=a^x$ .

$[1] y = log (x - 3)$ $[1]" "y=log(x-3)$

First we must convert this to exponential form.

$[2] \Leftrightarrow 10^{y} = x - 3$ $[2]" "hArr10^y=x-3$

Isolate $x$ $x$ by adding $3$ $3$ to both sides.

$[3] 10^{y} + 3 = x - 3 + 3$ $[3]" "10^y+3=x-3+3$

$[4] x = 10^{y} + 3$ $[4]" "x=10^y+3$

Finally, switch the positions of $x$ $x$ and $y$ $y$ to get the inverse function.

$[5] y = 10^{x} + 3$ $[5]" "color(blue)(y=10^x+3)$

What is the inverse of y=log(x−3)?y=log(x-3)? ?