What is the answer to \sqrt[a]{x}=2^{log_{3}(x)} ?

The answer to \sqrt[a]{x}=2^{log_{3}(x)} is x=1 {a 0}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\sqrt[a]{x}=2^{log_{3}(x)}

x = 1 {a < 0 or a > 0}

Solution steps

Apply log rules

\frac{lo g _{3} ( x )}{a} = lo g_{3} (x) lo g_{3} (2)

Multiply both sides by

a

\frac{lo g _{3} ( x )}{a} a = lo g_{3} (x) lo g_{3} (2) a

Simplify

lo g_{3} (x) = lo g_{3} (x) lo g_{3} (2) a

Move

lo g_{3} (x) lo g_{3} (2) a

to the left side

lo g_{3} (x) - lo g_{3} (x) lo g_{3} (2) a = 0

Factor

lo g_{3} (x) - lo g_{3} (x) lo g_{3} (2) a : lo g_{3} (x) (1 - a lo g_{3} (2))

lo g_{3} (x) (1 - a lo g_{3} (2)) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

lo g_{3} (x) = 0

Apply log rules

x = 1

Verify Solutions:

x = 1 {a < 0 or a > 0}

The solution is

x = 1 {a < 0 or a > 0}

lo g_{16} (x) = 2

lo g_{2} (x) = 25

2 - lo g_{3} (x - 4) = lo g_{3} (x - 2)

1.9 = - lo g_{10} (x)

lo g_{2} (x + 6) + lo g_{2} (x) = 4

What is the answer to \sqrt[a]{x}=2^{log_{3}(x)} ?
The answer to \sqrt[a]{x}=2^{log_{3}(x)} is x=1 {a<0\lor a>0}