Question

25 pointsWhich strategy below best describes how you would solve the following equation?logo x = log 4+ log, 8ООООExpress the equation in exponential form, set the exponents equal to each other and solve.Use the fact that since both sides of the equation have logarithms with the same base to set the expressions equal to each other and solve.Use the product rule to turn the right hand side of the equation into a single logarithm. Recognize that the resulting value is equal to x.Use the fact that the logs have the same base to add the expressions on the right side of the equation together. Express the results in exponential form, set the exponentsequal to each other and solve.PreviousNext

Answer 1

Since we have logarithms in base 6 in both sides, we have

`\log _6x=\log _64\cdot8`

because, one property of the logarithm (product rule) is

`\log _ba+\text{lob}_bc=\log _ba\cdot c`

since 4*8=32, we obtain

`\log _6x=\log _632`

by applying the inverse function to logarithms in both sides (logarithms have the same basis), the answer is

`x=32`