What is log_{3}(81x^3sqrt(1+x^2)) ?

The solution to log_{3}(81x^3sqrt(1+x^2)) is 4+3log_{3}(x)+log_{3}(sqrt(1+x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{3}(81x^3sqrt(1+x^2))

simplify

lo g_{3} (81 x^{3} 1 + x^{2})

4 + 3 lo g_{3} (x) + lo g_{3} (1 + x^{2})

Solution steps

lo g_{3} (81 x^{3} 1 + x^{2})

Factor the number:

81 = 3^{4}

= lo g_{3} (3^{4} x^{3} 1 + x^{2})

Apply log rule:

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

lo g_{3} (3^{4} x^{3} 1 + x^{2}) = lo g_{3} (3^{4}) + lo g_{3} (x^{3} 1 + x^{2})

= lo g_{3} (3^{4}) + lo g_{3} (x^{3} 1 + x^{2})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{3} (3^{4}) = 4

= 4 + lo g_{3} (x^{3} 1 + x^{2})

Simplify

lo g_{3} (x^{3} 1 + x^{2}) : 3 lo g_{3} (x) + lo g_{3} (1 + x^{2})

= 4 + (3 lo g_{3} (x) + lo g_{3} (1 + x^{2}))

Apply rule:

a + (b + c) = a + b + c

4 + (3 lo g_{3} (x) + lo g_{3} (1 + x^{2})) = 4 + 3 lo g_{3} (x) + lo g_{3} (1 + x^{2})

= 4 + 3 lo g_{3} (x) + lo g_{3} (1 + x^{2})

- lo g_{10} (4.35 \cdot 1 0^{- 6})

ln (\frac{( 70 - 95 )}{( 5 - 95 ) ( 1.9958 )})

ln (23) - ln (7)

ln (b 4 \frac{b}{1 - b})

lo g_{3} (\frac{1}{9} a^{3} b)

What is log_{3}(81x^3sqrt(1+x^2)) ?
The solution to log_{3}(81x^3sqrt(1+x^2)) is 4+3log_{3}(x)+log_{3}(sqrt(1+x^2))