Solve for x
x=100\log_{2}\left(3\right)-\frac{2}{3}\approx 157.829583405
Solve for x (complex solution)
x=\frac{i\pi n_{1}}{3\ln(2)}+100\log_{2}\left(3\right)-\frac{2}{3}
n_{1}\in \mathrm{Z}
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4^{3x+2}=18739277038847939886754019920358123424308469030992781557966909983211910963157763678726120154469030856807730587971859910379069087693119051085139566217370635083384943613868029545256897117998608156843699465093293765833141309526696357142600866935689483770877815014461194837692223879905132001
Use the rules of exponents and logarithms to solve the equation.
\log(4^{3x+2})=\log(18739277038847939886754019920358123424308469030992781557966909983211910963157763678726120154469030856807730587971859910379069087693119051085139566217370635083384943613868029545256897117998608156843699465093293765833141309526696357142600866935689483770877815014461194837692223879905132001)
Take the logarithm of both sides of the equation.
\left(3x+2\right)\log(4)=\log(18739277038847939886754019920358123424308469030992781557966909983211910963157763678726120154469030856807730587971859910379069087693119051085139566217370635083384943613868029545256897117998608156843699465093293765833141309526696357142600866935689483770877815014461194837692223879905132001)
The logarithm of a number raised to a power is the power times the logarithm of the number.
3x+2=\frac{\log(18739277038847939886754019920358123424308469030992781557966909983211910963157763678726120154469030856807730587971859910379069087693119051085139566217370635083384943613868029545256897117998608156843699465093293765833141309526696357142600866935689483770877815014461194837692223879905132001)}{\log(4)}
Divide both sides by \log(4).
3x+2=\log_{4}\left(18739277038847939886754019920358123424308469030992781557966909983211910963157763678726120154469030856807730587971859910379069087693119051085139566217370635083384943613868029545256897117998608156843699465093293765833141309526696357142600866935689483770877815014461194837692223879905132001\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
3x=300\log_{2}\left(3\right)-2
Subtract 2 from both sides of the equation.
x=\frac{300\log_{2}\left(3\right)-2}{3}
Divide both sides by 3.
Examples
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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