Question

Find the values of $x$ and $y$. If ${\log }_{10}(x-1)={\log }_{10}(y+4)$ and $x+y=6$.

Answer 1

It is given that ${\log }_{10}\left(x-1\right)={\log }_{10}\left(y+4\right)$, then,

$x-1=y+4$

$x-y=5$ (1)

And,

$x+y=6$ (2)

From equation (1) and equation (2),

$x=\frac{11}{2}$ and $y=\frac{1}{2}$.

Therefore, the values are $x=\frac{11}{2}$ and $y=\frac{1}{2}$.