What is log_{2}(75)-2log_{2}(5) ?

The solution to log_{2}(75)-2log_{2}(5) is log_{2}(3)

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simplify log_{2}(75)-2log_{2}(5)

simplify

lo g_{2} (75) - 2 lo g_{2} (5)

lo g_{2} (3)

Decimal Notation

1.58496 \dots

Solution steps

lo g_{2} (75) - 2 lo g_{2} (5)

Apply log rule:

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

- 2 lo g_{2} (5) = - lo g_{2} (5^{2})

= lo g_{2} (75) - lo g_{2} (5^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (75) - lo g_{2} (5^{2}) = lo g_{2} (\frac{75}{5 ^{2}})

= lo g_{2} (\frac{75}{5 ^{2}})

Cancel

\frac{75}{5 ^{2}} : 3

= lo g_{2} (3)

ln (x) + ln (x + 8)

lo g_{a} (2 x)

lo g_{10} (\frac{5 x}{y ^{3}})

lo g_{3} (A) + lo g_{3} (B)

What is log_{2}(75)-2log_{2}(5) ?
The solution to log_{2}(75)-2log_{2}(5) is log_{2}(3)