Question

1" title=" log(50) + log( \frac{x}{2} ) = 2" alt=" log(50) + log( \frac{x}{2} ) = 2" align="absmiddle" class="latex-formula">


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Answer 1

$\log50+\log\dfrac x2=2$

Condense the logarithms on the left into one:

$\log\left(50\cdot\dfrac x2\right)=\log(25x)=2$

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 $x$:

$x=\dfrac{100}4\implies\boxed{x=25}$