Question

What is the solution of log3x − 2125 = 3

Answer 1

the answer is x=7/3 hope this helps 

Answer 2

The solution for the given expression
`\log _(3x-2)\left(125\right)=3` is
`(7)/(3)`

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)=(\ln \left(b\right))/(\ln \left(a\right))`

`\log _(3x-2)\left(125\right)=(\ln \left(125\right))/(\ln \left(3x-2\right))`

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

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

We get,
`(\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,

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

Also,
`(\ln \left(125\right))/(3)=(\ln \left(5^3\right))/(3)=(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=(7)/(3)`

Thus, the solution for the given expression
`\log _(3x-2)\left(125\right)=3` is
`(7)/(3)`