Solve log4(x^2) log43=log415

Evaluate

lo g_{10} (4) \times x^{2} lo g_{10} (43) = lo g_{10} (415)

Multiply the numbers

lo g_{10} (4) \times lo g_{10} (43) \times x^{2} = lo g_{10} (415)

Divide both sides

\frac{lo g _{10} ( 4 ) \times lo g _{10} ( 43 ) \times x ^{2}}{lo g _{10} ( 4 ) \times lo g _{10} ( 43 )} = \frac{lo g _{10} ( 415 )}{lo g _{10} ( 4 ) \times lo g _{10} ( 43 )}

Divide the numbers

x^{2} = \frac{lo g _{4} ( 415 )}{lo g _{10} ( 43 )}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{lo g _{4} ( 415 )}{lo g _{10} ( 43 )}

Simplify the expression

x = \pm \frac{lo g _{4} ( 415 ) \times lo g _{10} ( 43 )}{lo g _{10} ( 43 )}

Separate the equation into 2 possible cases

x = \frac{lo g _{4} ( 415 ) \times lo g _{10} ( 43 )}{lo g _{10} ( 43 )} x = - \frac{lo g _{4} ( 415 ) \times lo g _{10} ( 43 )}{lo g _{10} ( 43 )}

Solve the equation

More Steps

x = \frac{\frac{l o g _{2} ( 415 ) \times l o g _{10} ( 43 )}{2}}{lo g _{10} ( 43 )} x = - \frac{lo g _{4} ( 415 ) \times lo g _{10} ( 43 )}{lo g _{10} ( 43 )}

Solve the equation

More Steps

x = \frac{\frac{l o g _{2} ( 415 ) \times l o g _{10} ( 43 )}{2}}{lo g _{10} ( 43 )} x = - \frac{\frac{l o g _{2} ( 415 ) \times l o g _{10} ( 43 )}{2}}{lo g _{10} ( 43 )}

Solution

x_{1} = - \frac{\frac{l o g _{2} ( 415 ) \times l o g _{10} ( 43 )}{2}}{lo g _{10} ( 43 )}, x_{2} = \frac{\frac{l o g _{2} ( 415 ) \times l o g _{10} ( 43 )}{2}}{lo g _{10} ( 43 )}

Alternative Form

x_{1} \approx - 1.631599, x_{2} \approx 1.631599

Solve the quadratic equation