How do you simplify ${log}_{8} (\sqrt[3]{\frac{x^{8}}{y^{7}}})$ $\log _ { 8} ( \root[ 3] { \frac { x ^ { 8} } { y ^ { 7} } } )$ ?

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How do you simplify ${log}_{8} (\sqrt[3]{\frac{x^{8}}{y^{7}}})$ $\log _ { 8} ( \root[ 3] { \frac { x ^ { 8} } { y ^ { 7} } } )$ ?

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Answer 1 · 2018-01-09T14:02:32

$\frac{1}{3} (8 {log}_{8} x - 7 {log}_{8} y)$ $1/3 (8 log_8 x - 7 log_8 y)$

Explanation:

Using the fact that $log (u^{v}) = v log (u)$ $log(u^v) = v log (u)$ and $log (\frac{u}{v}) = log (u) - log (v)$ $log(u/v) = log(u)-log(v)$ , we get:

${log}_{8} (\sqrt[3]{\frac{x^{8}}{y^{7}}})$ $log_8 ( root(3)(x^8 / y^7))$ = $\frac{1}{3} {log}_{8} (\frac{x^{8}}{y^{7}})$ $1/3 log_8 (x^8/y^7)$ =
$\frac{1}{3} ({log}_{8} x^{8} - {log}_{8} y^{7})$ $1/3 (log_8 x^8 - log_8 y^7)$ = $\frac{1}{3} (8 {log}_{8} x - 7 {log}_{8} y)$ $1/3 (8 log_8 x - 7 log_8 y)$

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How do you simplify ${log}_{8} (\sqrt[3]{\frac{x^{8}}{y^{7}}})$ $\log _ { 8} ( \root[ 3] { \frac { x ^ { 8} } { y ^ { 7} } } )$ ?

1 Answer

Explanation:

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How do you simplify log8(3√x8y7)\log _ { 8} ( \root[ 3] { \frac { x ^ { 8} } { y ^ { 7} } } )?

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How do you simplify ${log}_{8} (\sqrt[3]{\frac{x^{8}}{y^{7}}})$ $\log _ { 8} ( \root[ 3] { \frac { x ^ { 8} } { y ^ { 7} } } )$ ?