Question

`log(50) + log( (x)/(2) ) = 2`


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Answer 1

`\log50+\log\frac x2=2`

Condense the logarithms on the left into one:

`\log\left(50\cdot\frac x2\right)=\log(25x)=2`

Assuming the base of the logarithm is 10, write both sides as powers of 10. This lets us eliminate the logarithm:

`10^(\log(25x))=10^2\implies25x=100`

Divide both sides by 24 to solve for
`x`:

`x=\frac{100}4\implies\boxed{x=25}`