en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{2}(4^2*3^4)

Solution

simplify

lo g_{2} (4^{2} \cdot 3^{4})

Solution

4 + 4 lo g_{2} (3)

+1

Decimal Notation

10.33985 \dots

Solution steps

lo g_{2} (4^{2} \cdot 3^{4})

4^{2} = 2^{4}

= lo g_{2} (2^{4} \cdot 3^{4})

Apply log rule:

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

lo g_{2} (2^{4} \cdot 3^{4}) = lo g_{2} (2^{4}) + lo g_{2} (3^{4})

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

Apply log rule:

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

lo g_{2} (2^{4}) = 4

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{2} (3^{4}) = 4 lo g_{2} (3)

= 4 + 4 lo g_{2} (3)

Popular Examples

simplify-8\times 4 simplify

- 8 \times 4

simplify (sec(x))/(csc(x))+(csc(x))/(sec(x))simplify

\frac{sec ( x )}{csc ( x )} + \frac{csc ( x )}{sec ( x )}

simplify-log_{10}(0.00003)simplify

- lo g_{10} (0.00003)

simplify [(5^3)^4]^2 simplify

[(5^{3})^{4}]^{2}

simplify (103)+(-142)simplify

(103) + (- 142)

Frequently Asked Questions (FAQ)

What is log_{2}(4^2*3^4) ?
The solution to log_{2}(4^2*3^4) is 4+4log_{2}(3)