Solve 2log(8n^4) 6=10

Question

Solve the equation

n_{1} = - \frac{24 64 \times 1 0 ^{5}}{2}, n_{2} = \frac{24 64 \times 1 0 ^{5}}{2}

Alternative Form

n_{1} \approx - 0.96064, n_{2} \approx 0.96064

Evaluate

2 lo g_{10} (8 n^{4}) \times 6 = 10

Find the domain

More Steps

2 lo g_{10} (8 n^{4}) \times 6 = 10, n \neq = 0

Multiply the terms

12 lo g_{10} (8 n^{4}) = 10

Divide both sides

\frac{12 lo g _{10} ( 8 n ^{4} )}{12} = \frac{10}{12}

Divide the numbers

lo g_{10} (8 n^{4}) = \frac{10}{12}

Cancel out the common factor 2

lo g_{10} (8 n^{4}) = \frac{5}{6}

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

8 n^{4} = 1 0^{\frac{5}{6}}

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

8 n^{4} = 6 1 0^{5}

Divide both sides

\frac{8 n ^{4}}{8} = \frac{6 1 0 ^{5}}{8}

Divide the numbers

n^{4} = \frac{6 1 0 ^{5}}{8}

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

n = \pm 4 \frac{6 1 0 ^{5}}{8}

Simplify the expression

More Steps

n = \pm \frac{24 64 \times 1 0 ^{5}}{2}

Separate the equation into 2 possible cases

n = \frac{24 64 \times 1 0 ^{5}}{2} n = - \frac{24 64 \times 1 0 ^{5}}{2}

Check if the solution is in the defined range

n = \frac{24 64 \times 1 0 ^{5}}{2} n = - \frac{24 64 \times 1 0 ^{5}}{2}, n \neq = 0

Find the intersection of the solution and the defined range

n = \frac{24 64 \times 1 0 ^{5}}{2} n = - \frac{24 64 \times 1 0 ^{5}}{2}

Solution

n_{1} = - \frac{24 64 \times 1 0 ^{5}}{2}, n_{2} = \frac{24 64 \times 1 0 ^{5}}{2}

Alternative Form

n_{1} \approx - 0.96064, n_{2} \approx 0.96064

Show Solution