Question

Evaluate: log1255a.1/3b.1/2c. 2/3​

Answer 1

$\log_{125}(5)=\log_{5^3}(5)=\dfrac{1}{3}\log_5(5)=\dfrac{1}{3}\cdot1=\boxed{\dfrac{1}{3}}$

Hope this helps.

r3t40

Answer 2

Answer:

$\frac{1}{3}$

Step-by-step explanation:

Using the rule of logarithms

$log_{b}$ x = n ⇔ x = $b^{n}$

let $log_{125}$ 5 = n, then

5 = $125^{n}$

note that 125 = 5³ ⇒ $(5^3) ^{n}$ = $5^{3n}$

Since bases are equal ( both 5) equate the exponents

3n = 1 ( divide both sides by 3 )

n = $\frac{1}{3}$