Question

If 3 to the power y = x then y = ?

Answer 1

Answer:

$y=\log_3(x)$

Step-by-step explanation:

$3^y=x$

$\ln(3^y)=\ln(x)$

$y\ln(3)=\ln(x)$

$y=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}$

but if

$f(x)=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}$

then since

$f(3)=\frac{\displaystyle\ln(3)}{\displaystyle\ln(3)}=1$

$f(x)=\log_3(x)$

so

$y=\log_3(x)$

or

$3^y=x$

$\log_3(3^y)=\log_3(x)$

$y\log_3(3)=\log_3(x)$

$\text{but }\,\log_3(3)=1, \text{so,}$

$y=\log_3(x)$