Solve 2log49x=1/2

Evaluate

2 lo g_{10} (49 x) = \frac{1}{2}

Find the domain

More Steps

2 lo g_{10} (49 x) = \frac{1}{2}, x > 0

Multiply by the reciprocal

2 lo g_{10} (49 x) \times \frac{1}{2} = \frac{1}{2} \times \frac{1}{2}

Multiply

lo g_{10} (49 x) = \frac{1}{2} \times \frac{1}{2}

Multiply

More Steps

lo g_{10} (49 x) = \frac{1}{4}

Convert the logarithm into exponential form using the fact that lo g_{a} x = b is equal to x = a^{b}

49 x = 1 0^{\frac{1}{4}}

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

49 x = 410

Divide both sides

\frac{49 x}{49} = \frac{4 10}{49}

Divide the numbers

x = \frac{4 10}{49}

Check if the solution is in the defined range

x = \frac{4 10}{49}, x > 0

Solution

x = \frac{4 10}{49}

Alternative Form

x \approx 0.036291

Solve the equation