Solve the logarithmic equation $\log_{6}\left(\sqrt[3]{x^7}\right)=\log_{6}\left(4279.2977\right)$

Got another answer? Verify it here!

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log6(x^7^(1/3))=log6(4279.297715). Simplify \sqrt[3]{x^7} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 7 and n equals \frac{1}{3}. Multiply the fraction and term in 7\cdot \left(\frac{1}{3}\right). For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b. Removing the variable's exponent raising both sides of the equation to the power of \frac{3}{7}.