How do you find the inverse of $y = 2^{1.5 x + 3}$ $y= 2^(1.5x+3)$ ?

Question

1726 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-25T13:20:08

$f^{- 1} (x) = \frac{{log}_{2} x - 3}{1.5}$ $f^-1(x)=(log_2x-3)/1.5$

$[1] f (x) = 2^{1.5 x + 3}$ $[1]" "f(x)=2^(1.5x+3)$

$[2] y = 2^{1.5 x + 3}$ $[2]" "y=2^(1.5x+3)$

Switch $x$ $x$ and $y$ $y$ .

$[3] x = 2^{1.5 y + 3}$ $[3]" "x=2^(1.5y+3)$

Convert this to logarithmic form.

$[4] \Leftrightarrow {log}_{2} x = 1.5 y + 3$ $[4]" "hArrlog_2x=1.5y+3$

Subtract 3 from both sides.

$[5] {log}_{2} x - 3 = 1.5 y$ $[5]" "log_2x-3=1.5y$

Divide both sides by $1.5$ $1.5$ .

$[6] \frac{{log}_{2} x - 3}{1.5} = y$ $[6]" "(log_2x-3)/1.5=y$

$[7] f^{- 1} (x) = \frac{{log}_{2} x - 3}{1.5}$ $[7]" "color(blue)(f^-1(x)=(log_2x-3)/1.5)$

How do you find the inverse of y=21.5x+3y= 2^(1.5x+3)?