Question

Express in logarithmic form for the base. x y = P

Answer 1

So

$x^y=P$

remember
$a^b=c$ translates to $log_a(c)=b$
basically, the power that a must be raised to to obtain c is b

so
$x^y=P$ translates to $log_x(P)=y$

Answer 2

Answer:

$y=\text{log}_x(P)$

Step-by-step explanation:

We are asked to write our given exponential equation $x^y=P$ as logarithmic form.

First of all, we will take logarithm of both sides of our equation.

$\text{log}(x^y)=\text{log}(P)$

Using logarithm property $\text{log}(a^b)=b\cdot \text{log}(a)$ we will get,

$y\cdot \text{log}(x)=\text{log}(P)$

Dividing both sides by $\text{log}(x)$, we will get:

$\frac{y\cdot \text{log}(x)}{ \text{log}(x)}=\frac{\text{log}(P)}{ \text{log}(x)}$

$y=\frac{\text{log}(P)}{ \text{log}(x)}$

Using property $\frac{\text{log}_x(a)}{\text{log}_x(b)}=\text{log}_b(a)$, we will get,

$y=\text{log}_x(P)$

Therefore, our required expression would be $y=\text{log}_x(P)$.