How do you write the equation ${log}_{7} (\frac{1}{2401}) = - 4$ $log_7 (1/2401)=-4$ into exponential form?

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Answer 1 · 2016-12-20T03:41:40

$7^{- 4} = \frac{1}{2401}$ $7^-4=1/2401$

Write ${log}_{7} (\frac{1}{2401}) = - 4$ $log_7(1/2401)=-4$ as an exponential.

Use the rule ${log}_{b} x = a a a \Rightarrow a a x = b^{a}$ $log_bx=a color(white)(aa)=> color(white)(aa)x=b^a$

${log}_{7} (\frac{1}{2401}) = - 4 a a \Rightarrow a a 7^{- 4} = \frac{1}{2401}$ $log_7(1/2401)=-4color(white)(aa)=>color(white)(aa)7^-4=1/2401$

Note that the $7$ $7$ is the base of the log and the base of the exponential. And, the "answer" to a log equation is the exponent of the exponential.

How do you write the equation log7(12401)=−4log_7 (1/2401)=-4 into exponential form?