Question

What is the solution to this equation?10g* +108g3 = 108g(= + 1)

Answer 1

We cal solve the equation using logarithms properties:

`\log_6x+\log_63=\log_6(x+1)`

Use the next logarithm rule:

`\log_bM+\log_bN=\log_bMN`

Then,

`\log_6x+\log_63=\log_63x`

Hence, we have the next equation:

`\log_63x=\log_6(x+1)`

Now, use the equality property:

`\begin{gathered} if\text{ }\log_bm=\log_bn \\ Then \\ m=n \end{gathered}`

Hence,

`\begin{gathered} 3x=x+1 \\ \end{gathered}`

Solve for:

`\begin{gathered} 3x-x=1 \\ 2x=1 \\ x=(1)/(2) \end{gathered}`

Hence, the correct answer is 1/2.

The answer is option x= 1/2.