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

Question

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

$(a)$ $xz$
$(b)$ $z/x$
$(c)$ $z+x$
$(d)$ $z-x$

I searched on internet about correct answer and it was $(b)$ $z/x$ , but I don't know why $(b)$ is correct. I think that all the answers listed are incorrect.

2353 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-15T07:42:09

I got $a=y^z/y^x=y^(z-x)$

$6a=3.5=>a=3.5/6$

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:

$a=y^z/y^x=y^(z-x)$