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Solve for x
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Solve for x (complex solution)
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180=2^{x}\times 9\times 5
Calculate 3 to the power of 2 and get 9.
180=2^{x}\times 45
Multiply 9 and 5 to get 45.
2^{x}\times 45=180
Swap sides so that all variable terms are on the left hand side.
2^{x}=\frac{180}{45}
Divide both sides by 45.
2^{x}=4
Divide 180 by 45 to get 4.
\log(2^{x})=\log(4)
Take the logarithm of both sides of the equation.
x\log(2)=\log(4)
The logarithm of a number raised to a power is the power times the logarithm of the number.
x=\frac{\log(4)}{\log(2)}
Divide both sides by \log(2).
x=\log_{2}\left(4\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).