What is expand log_{5}(375)-log_{5}(3) ?

The solution to expand log_{5}(375)-log_{5}(3) is 3

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expand log_{5}(375)-log_{5}(3)

expand

lo g_{5} (375) - lo g_{5} (3)

3

Solution steps

lo g_{5} (375) - lo g_{5} (3)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{5} (375) - lo g_{5} (3) = lo g_{5} (\frac{375}{3})

= lo g_{5} (\frac{375}{3})

Divide the numbers:

\frac{375}{3} = 125

= lo g_{5} (125)

Rewrite

125

in power-base form:

125 = 5^{3}

= lo g_{5} (5^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{5} (5^{3}) = 3 lo g_{5} (5)

= 3 lo g_{5} (5)

Apply log rule:

lo g_{a} (a) = 1

lo g_{5} (5) = 1

= 3 \cdot 1

Multiply the numbers:

3 \cdot 1 = 3

= 3

\frac{9 ( 2 k + 1 )}{2 k + 3}

\frac{13000 ( 65 - 3 x ^{2} )}{( 65 + x ^{3} )}

(sin (x) + cos (x)) \cdot (sin (y) + cos (y))

- \frac{1}{4} (t + 3 ln ∣ t ∣) + C

What is expand log_{5}(375)-log_{5}(3) ?
The solution to expand log_{5}(375)-log_{5}(3) is 3