Solve log3x^2/4=log3^25

Question

\frac{lo g _{10} ( 3 x ^{2} )}{4} = lo g_{10} (3^{2} \times 5)

Solve the equation

x_{1} = - 6753, x_{2} = 6753

Alternative Form

x_{1} \approx - 1169.134295, x_{2} \approx 1169.134295

Evaluate

\frac{lo g _{10} ( 3 x ^{2} )}{4} = lo g_{10} (3^{2} \times 5)

Find the domain

More Steps

\frac{lo g _{10} ( 3 x ^{2} )}{4} = lo g_{10} (3^{2} \times 5), x \neq = 0

Multiply the terms

More Steps

\frac{lo g _{10} ( 3 x ^{2} )}{4} = lo g_{10} (45)

Cross multiply

lo g_{10} (3 x^{2}) = 4 lo g_{10} (45)

Evaluate the logarithm

3 x^{2} = 4 5^{4}

Divide both sides

\frac{3 x ^{2}}{3} = \frac{4 5 ^{4}}{3}

Divide the numbers

x^{2} = \frac{4 5 ^{4}}{3}

Divide the numbers

More Steps

x^{2} = 1366875

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

x = \pm 1366875

Simplify the expression

More Steps

x = \pm 6753

Separate the equation into 2 possible cases

x = 6753 x = - 6753

Check if the solution is in the defined range

x = 6753 x = - 6753, x \neq = 0

Find the intersection of the solution and the defined range

x = 6753 x = - 6753

Solution

x_{1} = - 6753, x_{2} = 6753

Alternative Form

x_{1} \approx - 1169.134295, x_{2} \approx 1169.134295

Show Solution