Solve for a
a=\frac{4}{5}-b
Solve for b
b=\frac{4}{5}-a
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32^{a+b}=16
Use the rules of exponents and logarithms to solve the equation.
\log(32^{a+b})=\log(16)
Take the logarithm of both sides of the equation.
\left(a+b\right)\log(32)=\log(16)
The logarithm of a number raised to a power is the power times the logarithm of the number.
a+b=\frac{\log(16)}{\log(32)}
Divide both sides by \log(32).
a+b=\log_{32}\left(16\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
a=\frac{4}{5}-b
Subtract b from both sides of the equation.
32^{b+a}=16
Use the rules of exponents and logarithms to solve the equation.
\log(32^{b+a})=\log(16)
Take the logarithm of both sides of the equation.
\left(b+a\right)\log(32)=\log(16)
The logarithm of a number raised to a power is the power times the logarithm of the number.
b+a=\frac{\log(16)}{\log(32)}
Divide both sides by \log(32).
b+a=\log_{32}\left(16\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
b=\frac{4}{5}-a
Subtract a from both sides of the equation.
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