Question

Find the inverse of 3 + 7^x

Answer 1

3+7^x=y
y-3=7^x
taking ln on both sides
ln7^x=ln(y-3)
xln7=ln(y-3)
x=ln(y-3)/ln7
switch x with y and y with x
y=ln(x-3)/ln7

Answer 2

my teacher got f-1(x)=log7(x-3) dont know how

Answer 3

because whynot gave you an answer you could actually use, since you have the natural log (ln) on your calculator.
your teacher just said the inverse of
\[7^x\] is
\[\log_7(x)\]

Answer 4

your teacher put solved
\[x=3+7^y\] for y in two steps:
\[x-3=7^y\]
\[\log_7(x-3)=y\]

Answer 5

in other words saying
\[b^x=y\] is the same as saying
\[x=\log_b(y)\]

Answer 6

o ok makes sense thanks for the help

Answer 7

yw