Question 262500
pls help...if 9^x=27^y and 8^y=16^z, then what is the value of x:y:z
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{{{9^x=27^y}}}
{{{(3^2)^x=(3^3)^y}}}
{{{3^(2x)=3^(3y)}}}
The bases are equal, positive, and not 1, so
the exponents are equal
{{{2x=3y}}}

Divide both sides by 2y

{{{x/y=3/2}}}

{{{"x:y"="3:2"}}}

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{{{8^y=16^z}}}
{{{(2^3)^y=(2^4)^z}}}
{{{2^(3y)=2^(4z)}}}
The bases are equal, positive, and not 1, so
the exponents are equal
{{{3y=4z}}}

Divide both sides by 3z

{{{y/z=4/3}}}

{{{"y:z"="4:3"}}}

{{{"x:y"="3:2"}}} and {{{"y:z"="4:3"}}}

y corresponds to 2 in the first ratio
but y corresponds to 4 in the second ratio.
The least common multiple is 4, so change
the first ratio to 

{{{"x:y"="6:4"}}} 

and we now have

{{{"x:y"="6:4"}}} and {{{"y:z"="4:3"}}}

so that y corresponds to the same number, 4,
in both ratios, and now we can write:

{{{"x:y:z"="6:4:3"}}}

Edwin<pre>