Mathematics: What is 2log5(5x^3)+(1/3)log5((x^2)+6) written as a single logarithm?

What is 2log5(5x^3)+(1/3)log5((x^2)+6) written - id2553135261707341, kloeyknows7323

halfpint1168

16.03.2022

= $log_5\ (25\ x^6\ \sqrt[3]{x^2+6})$

Step-by-step explanation:

Given log expression $2log_5(5x^3)+\frac{1}{3} log_5((x^2)+6)$ .

First we would apply log rule of exponents : nlog_b(a) = log_b(a)^n

$2log_5(5x^3)+\frac{1}{3} log_5((x^2)+6) = log_5(5x^3)^2+ log_5((x^2)+6)^{\frac{1}{3}}$ .

Converting rational exponent into radical form, we get

$log_5(5x^3)^2+ log_5\sqrt[3]{((x^2)+6)}$ .

Simplifying $(5x^3)^2 = 5^2x^{3\times 2} = 25x^6$

= $log_5(25x^6)+ log_5\sqrt[3]{((x^2)+6)}$ .

Applying sum of logs rule $log_b(m)+log_b(n) = log_b(m\times n)$ .

= $log_5\ (25\ x^6\ \sqrt[3]{x^2+6})$

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dtaylor7755

08.08.2022

uhhh i'll try lol

Explanation:

i expect to lose

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