Solve for a
a=5-b
Solve for b
b=5-a
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3^{a+b}=243
Use the rules of exponents and logarithms to solve the equation.
\log(3^{a+b})=\log(243)
Take the logarithm of both sides of the equation.
\left(a+b\right)\log(3)=\log(243)
The logarithm of a number raised to a power is the power times the logarithm of the number.
a+b=\frac{\log(243)}{\log(3)}
Divide both sides by \log(3).
a+b=\log_{3}\left(243\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
a=5-b
Subtract b from both sides of the equation.
3^{b+a}=243
Use the rules of exponents and logarithms to solve the equation.
\log(3^{b+a})=\log(243)
Take the logarithm of both sides of the equation.
\left(b+a\right)\log(3)=\log(243)
The logarithm of a number raised to a power is the power times the logarithm of the number.
b+a=\frac{\log(243)}{\log(3)}
Divide both sides by \log(3).
b+a=\log_{3}\left(243\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
b=5-a
Subtract a from both sides of the equation.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}