Answer:
[tex]y=\text{log}_x(P)[/tex]
Step-by-step explanation:
We are asked to write our given exponential equation [tex]x^y=P[/tex] as logarithmic form.
First of all, we will take logarithm of both sides of our equation.
[tex]\text{log}(x^y)=\text{log}(P)[/tex]
Using logarithm property [tex]\text{log}(a^b)=b\cdot \text{log}(a)[/tex] we will get,
[tex]y\cdot \text{log}(x)=\text{log}(P)[/tex]
Dividing both sides by [tex]\text{log}(x)[/tex], we will get:
[tex]\frac{y\cdot \text{log}(x)}{ \text{log}(x)}=\frac{\text{log}(P)}{ \text{log}(x)}[/tex]
[tex]y=\frac{\text{log}(P)}{ \text{log}(x)}[/tex]
Using property [tex]\frac{\text{log}_x(a)}{\text{log}_x(b)}=\text{log}_b(a)[/tex], we will get,
[tex]y=\text{log}_x(P)[/tex]
Therefore, our required expression would be [tex]y=\text{log}_x(P)[/tex].
