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Solve for x (complex solution)
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\sqrt{633825300114114700748351602688+2^{99}}=3^{x}
Calculate 2 to the power of 99 and get 633825300114114700748351602688.
\sqrt{633825300114114700748351602688+633825300114114700748351602688}=3^{x}
Calculate 2 to the power of 99 and get 633825300114114700748351602688.
\sqrt{1267650600228229401496703205376}=3^{x}
Add 633825300114114700748351602688 and 633825300114114700748351602688 to get 1267650600228229401496703205376.
1125899906842624=3^{x}
Calculate the square root of 1267650600228229401496703205376 and get 1125899906842624.
3^{x}=1125899906842624
Swap sides so that all variable terms are on the left hand side.
\log(3^{x})=\log(1125899906842624)
Take the logarithm of both sides of the equation.
x\log(3)=\log(1125899906842624)
The logarithm of a number raised to a power is the power times the logarithm of the number.
x=\frac{\log(1125899906842624)}{\log(3)}
Divide both sides by \log(3).
x=\log_{3}\left(1125899906842624\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).