Question

What is the solution of log3x − 2125 = 3

Answer 1

Answer:

The solution for the given expression $\log _{3x-2}\left(125\right)=3$ is $\frac{7}{3}$

Step-by-step explanation:

Given : Expression $\log _{3x-2}\left(125\right)=3$

We have to find the solution for the given expression $\log _{3x-2}\left(125\right)=3$

Consider the given expression $\log _{3x-2}\left(125\right)=3$

Apply log rule, $\log _a\left(b\right)=\frac{\ln \left(b\right)}{\ln \left(a\right)}$

$\log _{3x-2}\left(125\right)=\frac{\ln \left(125\right)}{\ln \left(3x-2\right)}$

$\frac{\ln \left(125\right)}{\ln \left(3x-2\right)}=3$

Multiply both side by $\ln \left(3x-2\right)$

We get, $\frac{\ln \left(125\right)}{\ln \left(3x-2\right)}\ln \left(3x-2\right)=3\ln \left(3x-2\right)$

Simplify , we have,

$\ln \left(125\right)=3\ln \left(3x-2\right)$

Divide both sie by 3, we get,

$\frac{3\ln \left(3x-2\right)}{3}=\frac{\ln \left(125\right)}{3}$

Also, $\frac{\ln \left(125\right)}{3}=\frac{\ln \left(5^3\right)}{3}=\frac{3\ln \left(5\right)}{3}=\ln(5)$

Thus, $\ln \left(3x-2\right)=\ln \left(5\right)$

When logs have same base, we have,

$\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)$

Thus, $3x - 2 = 5$

Add 2 both sides, we have,

$3x = 7$

Divide both side by 3, we have,

$x=\frac{7}{3}$

Thus, the solution for the given expression $\log _{3x-2}\left(125\right)=3$ is $\frac{7}{3}$

Answer 2

The answer is x=7/3 hope this helps