Question

Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. logx 36 = 2

Answer 1

Answer:

$x=6$

Step-by-step explanation:

We have been given a logarithmic equation $\text{log}_x(36)=2$. We are asked to solve our given equation.

Using log rule $\text{log}_a(b)=\frac{\text{ln}(b)}{\text{ln}(a)}$, we will get:

$\text{log}_x(36)=\frac{\text{ln}(36)}{\text{ln}(x)}$

Substituting back this value, we will get:

$\frac{\text{ln}(36)}{\text{ln}(x)}=2$

Multiply both sides by $\text{ln}(x)$:

$\frac{\text{ln}(36)}{\text{ln}(x)}\times\text{ln}(x)=2\times\text{ln}(x)$

$\text{ln}(36)=2\times\text{ln}(x)$

Switch sides:

$2\times\text{ln}(x)=\text{ln}(36)$

$2\times\text{ln}(x)=\text{ln}(6^2)$

Using property $\text{log}_a(x^b)=b\cdot \text{log}_a(x)$, we will get:

$2\times\text{ln}(x)=2\cdot \text{ln}(6)$

$\frac{2\times\text{ln}(x)}{2}=\frac{2\cdot \text{ln}(6)}{2}$

$\text{ln}(x)=\text{ln}(6)$

Since base of both sides are equal, therefore, the value of x is 6.