What is 2log_{10}(2)+3log_{10}(3)-2log_{10}(6) ?

The solution to 2log_{10}(2)+3log_{10}(3)-2log_{10}(6) is log_{10}(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2log_{10}(2)+3log_{10}(3)-2log_{10}(6)

simplify

2 lo g_{10} (2) + 3 lo g_{10} (3) - 2 lo g_{10} (6)

lo g_{10} (3)

Decimal Notation

0.47712 \dots

Solution steps

2 lo g_{10} (2) + 3 lo g_{10} (3) - 2 lo g_{10} (6)

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

3 lo g_{10} (3) = lo g_{10} (3^{3})

- 2 lo g_{10} (6) = - lo g_{10} (6^{2})

= lo g_{10} (2^{2}) + lo g_{10} (3^{3}) - lo g_{10} (6^{2})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (2^{2}) + lo g_{10} (3^{3}) = lo g_{10} (2^{2} \cdot 3^{3})

= lo g_{10} (2^{2} \cdot 3^{3}) - lo g_{10} (6^{2})

Apply log rule:

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

lo g_{10} (2^{2} \cdot 3^{3}) - lo g_{10} (6^{2}) = lo g_{10} (\frac{2 ^{2} \cdot 3 ^{3}}{6 ^{2}})

= lo g_{10} (\frac{2 ^{2} \cdot 3 ^{3}}{6 ^{2}})

Cancel

\frac{2 ^{2} \cdot 3 ^{3}}{6 ^{2}} : 3

= lo g_{10} (3)

lo g_{10} (\frac{a ^{5} a ^{2} b}{( ab ) ^{2}})

lo g_{10} (y^{5} x)

lo g_{a} (\frac{y ^{5} w ^{2}}{x ^{4} z ^{3}})

ln (3 arccos (x))

lo g_{4} (3) - lo g_{4} (7)

What is 2log_{10}(2)+3log_{10}(3)-2log_{10}(6) ?
The solution to 2log_{10}(2)+3log_{10}(3)-2log_{10}(6) is log_{10}(3)