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Popular >

simplify log_{sqrt(2)}(8)

Solution

simplify

lo g_{2} (8)

Solution

6

Solution steps

lo g_{2} (8)

Apply radical rule:

a = a^{\frac{1}{2}}

2 = 2^{\frac{1}{2}}

= lo g_{2^{\frac{1}{2}}} (8)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{\frac{1}{2}}} (8) = \frac{1}{\frac{1}{2}} lo g_{2} (8)

= \frac{1}{\frac{1}{2}} lo g_{2} (8)

Factor the number:

8 = 2^{3}

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

Apply log rule:

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

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

= \frac{1}{\frac{1}{2}} \cdot 3

\frac{1}{\frac{1}{2}} \cdot 3 = 6

= 6

Popular Examples

C(42)=((42)^2)/(3025-55(42))

C (42) = \frac{( 42 ) ^{2}}{3025 - 55 ( 42 )}

(y^2)/5 =(y+10)/3

\frac{y ^{2}}{5} = \frac{y + 10}{3}

simplify 1/2*300 simplify

\frac{1}{2} \cdot 300

factor 4x^2+12x factor

4 x^{2} + 12 x

x^{2} + 11 x + 9 = 5 x

Frequently Asked Questions (FAQ)

What is log_{sqrt(2)}(8) ?
The solution to log_{sqrt(2)}(8) is 6