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

Answer:[tex]x=6[/tex]Step-by-step explanation:We have been given a logarithmic equation [tex]\text{log}_x(36)=2[/tex]. We are asked to solve our given equation.Using log rule [tex]\text{log}_a(b)=\frac{\text{ln}(b)}{\text{ln}(a)}[/tex], we will get:[tex]\text{log}_x(36)=\frac{\text{ln}(36)}{\text{ln}(x)}[/tex]Substituting back this value, we will get:[tex]\frac{\text{ln}(36)}{\text{ln}(x)}=2[/tex]Multiply both sides by [tex]\text{ln}(x)[/tex]:[tex]\frac{\text{ln}(36)}{\text{ln}(x)}\times\text{ln}(x)=2\times\text{ln}(x)[/tex][tex]\text{ln}(36)=2\times\text{ln}(x)[/tex]Switch sides:[tex]2\times\text{ln}(x)=\text{ln}(36)[/tex] [tex]2\times\text{ln}(x)=\text{ln}(6^2)[/tex] Using property [tex]\text{log}_a(x^b)=b\cdot \text{log}_a(x)[/tex], we will get:[tex]2\times\text{ln}(x)=2\cdot \text{ln}(6)[/tex] [tex]\frac{2\times\text{ln}(x)}{2}=\frac{2\cdot \text{ln}(6)}{2}[/tex] [tex]\text{ln}(x)=\text{ln}(6)[/tex] Since base of both sides are equal, therefore, the value of x is 6.