 # Describe the strategy you would use to solve \log_{6}x-\log_{6}4+\log_{6}8 coexpennan 2021-09-27 Answered
Describe the strategy you would use to solve $$\displaystyle{{\log}_{{{6}}}{x}}-{{\log}_{{{6}}}{4}}+{{\log}_{{{6}}}{8}}$$.
a. Use the product rule to turn the right side of the equation into a single logarithm. Recognize that the resulting value is equal to x.
b. Express the equation in exponential form, set the exponents equal to each other and solve.
c. 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 exponents equal to each other and solve.
d. Use the fact that since both sides of the equations have logarithms with the same base to set the expressions equal to each other and solve.

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$$\displaystyle{{\log}_{{{6}}}{x}}={{\log}_{{{6}}}{4}}+{{\log}_{{{6}}}{8}}$$
$$\displaystyle{{\log}_{{{6}}}{x}}={{\log}_{{{6}}}{\left({32}\right)}}{\left\lbrace{{\log}_{{{c}}}{a}}+{{\log}_{{{c}}}{b}}={{\log}_{{{c}}}{\left({a}{b}\right)}}\right\rbrace}$$ Product rule.
$$\displaystyle{x}={32}$$
Option A is correct.