System of Equations With Exponents
By Emily Wilson •
What are the steps to solving a system of equations when $x$ and $y$ are exponents? Here is the problem to solve for $x$ and $y$.
$$8^{3x}=4^{2y}$$
$$x-y=5$$
$\endgroup$1 Answer
$\begingroup$Take the logarithm on both sides of the first equation to obtain $3x\ln 8=2y\ln 4$.
In this case, since both $8$ and $4$ are powers of $2$, an easier method is to write the first equation as $2^{9x}=2^{4y}$ so that $9x=4y$.
Using either way, one ends up with a pair of simultaneous linear equations to solve.
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