What is 2/3 log_{10}(27)+log_{10}(x)+log_{10}(x) ?

The solution to 2/3 log_{10}(27)+log_{10}(x)+log_{10}(x) is log_{10}(9x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2/3 log_{10}(27)+log_{10}(x)+log_{10}(x)

simplify

\frac{2}{3} lo g_{10} (27) + lo g_{10} (x) + lo g_{10} (x)

lo g_{10} (9 x^{2})

Solution steps

\frac{2}{3} lo g_{10} (27) + lo g_{10} (x) + lo g_{10} (x)

Add similar elements:

lo g_{10} (x) + lo g_{10} (x) = 2 lo g_{10} (x)

= \frac{2}{3} lo g_{10} (27) + 2 lo g_{10} (x)

\frac{2}{3} lo g_{10} (27) = 2 lo g_{10} (3)

= 2 lo g_{10} (3) + 2 lo g_{10} (x)

2 lo g_{10} (3) = lo g_{10} (3^{2})

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

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

Apply log rule:

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

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

= lo g_{10} (3^{2} x^{2})

Simplify

3^{2} x^{2} : 9 x^{2}

= lo g_{10} (9 x^{2})

- (3 ln (2) + ln (3))

lo g_{10} (\frac{x ^{3}}{( x + 6 ) ^{5}})

ln (\frac{1 + sin ( x )}{cos ( x )})

lo g_{10} (\frac{9 a ^{16}}{b ^{2}})

What is 2/3 log_{10}(27)+log_{10}(x)+log_{10}(x) ?
The solution to 2/3 log_{10}(27)+log_{10}(x)+log_{10}(x) is log_{10}(9x^2)