# If Log_y6=x, Log_y3.5=z and 6a=3.5 then a=??

## If $L o {g}_{y} 6 = x$, $L o {g}_{y} 3.5 = z$ and $6 a = 3.5$ then a=?? $\left(a\right)$ $x z$ $\left(b\right)$ $\frac{z}{x}$ $\left(c\right)$ $z + x$ $\left(d\right)$ $z - x$ I searched on internet about correct answer and it was $\left(b\right)$ $\frac{z}{x}$, but I don't know why $\left(b\right)$ is correct. I think that all the answers listed are incorrect.

I got $a = {y}^{z} / {y}^{x} = {y}^{z - x}$

#### Explanation:

$6 a = 3.5 \implies a = \frac{3.5}{6}$

We're told that

log_y6=x; log_y3.5=z

We can rearrange these equations to put them into exponential form:

y^x=6; y^z=3.5

And substitute in the values:

$a = {y}^{z} / {y}^{x} = {y}^{z - x}$