What is 3(2log_{10}(2A)-5log_{10}(2B)) ?

The solution to 3(2log_{10}(2A)-5log_{10}(2B)) is 3log_{10}((A^2)/(8B^5))

Popular >

simplify 3(2log_{10}(2A)-5log_{10}(2B))

simplify

3 (2 lo g_{10} (2 A) - 5 lo g_{10} (2 B))

3 lo g_{10} (\frac{A ^{2}}{8 B ^{5}})

Solution steps

3 (2 lo g_{10} (2 A) - 5 lo g_{10} (2 B))

2 lo g_{10} (2 A) = lo g_{10} ((2 A)^{2})

- 5 lo g_{10} (2 B) = - lo g_{10} ((2 B)^{5})

= 3 (lo g_{10} ((2 A)^{2}) - lo g_{10} ((2 B)^{5}))

Apply log rule:

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

lo g_{10} ((2 A)^{2}) - lo g_{10} ((2 B)^{5}) = lo g_{10} (\frac{( 2 A ) ^{2}}{( 2 B ) ^{5}})

= 3 lo g_{10} (\frac{( 2 A ) ^{2}}{( 2 B ) ^{5}})

Cancel

\frac{( 2 A ) ^{2}}{( 2 B ) ^{5}} : \frac{A ^{2}}{8 B ^{5}}

= 3 lo g_{10} (\frac{A ^{2}}{8 B ^{5}})

ln (\frac{6 + 0.5}{7 \cdot 0.5})

\frac{1}{9} ln (\frac{6}{5})

lo g_{7} (4) \cdot lo g_{2} (5) + lo g_{7} (\frac{49}{25})

\frac{1}{3} lo g_{3} (2)

\frac{\partial}{\partial x} (x^{2} y) + ln (x y^{2})

What is 3(2log_{10}(2A)-5log_{10}(2B)) ?
The solution to 3(2log_{10}(2A)-5log_{10}(2B)) is 3log_{10}((A^2)/(8B^5))