Question

solve for c. approximate by rounding your answer to three decimal places.
$6 \log_{7}(c) = \log_{7}(47)$
show your work here
$c = $

solve for n. approximate by rounding your answer to three decimal places.
$6 \log_{11}(n) = \log_{11}(128)$
show your work here
hint: to add an exponent ($x^y$), type \exponent\ or press \^\
$n = $

Explanation:

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Solving for $c$

Step1: Apply log power rule

$\log_{7}(c^6) = \log_{7}(47)$

Step2: Equate arguments of logs

$c^6 = 47$

Step3: Take 6th root of both sides

$c = 47^{\frac{1}{6}}$

Step4: Calculate and round

$c = e^{\frac{\ln(47)}{6}} \approx 1.809$

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Solving for $n$

Step1: Apply log power rule

$\log_{11}(n^6) = \log_{11}(128)$

Step2: Equate arguments of logs

$n^6 = 128$

Step3: Take 6th root of both sides

$n = 128^{\frac{1}{6}}$

Step4: Calculate and round

$n = e^{\frac{\ln(128)}{6}} \approx 2.046$

Answer:

$c = 1.809$
$n = 2.046$