What is the answer to (log_{2}(x))^3=log_{8}(x) ?

The answer to (log_{2}(x))^3=log_{8}(x) is x=1,x= 1/(8^{\frac{1){3sqrt(3)}}},x=8^{1/(3sqrt(3))}

Solve for x: (log_{2}(x))^3=log_{8}(x)

The solution is x=1,x= 1/(8^{\frac{1){3sqrt(3)}}},x=8^{1/(3sqrt(3))}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(lo g_{2} (x))^{3} = lo g_{8} (x)

x = 1, x = \frac{1}{8 ^{\frac{1}{3 3}}}, x = 8^{\frac{1}{3 3}}

Solution steps

(lo g_{2} (x))^{3} = lo g_{8} (x)

Apply log rules

27 lo g_{8} (x)^{3} = lo g_{8} (x)

Rewrite the equation with

lo g_{8} (x) = u

27 u^{3} = u

Solve

27 u^{3} = u : u = 0, u = - \frac{1}{3 3}, u = \frac{1}{3 3}

u = 0, u = - \frac{1}{3 3}, u = \frac{1}{3 3}

Substitute back

u = lo g_{8} (x),

solve for

x

Solve

lo g_{8} (x) = 0 : x = 1

Solve

lo g_{8} (x) = - \frac{1}{3 3} : x = \frac{1}{8 ^{\frac{1}{3 3}}}

Solve

lo g_{8} (x) = \frac{1}{3 3} : x = 8^{\frac{1}{3 3}}

x = 1, x = \frac{1}{8 ^{\frac{1}{3 3}}}, x = 8^{\frac{1}{3 3}}

Verify Solutions:

x = 1

True

, x = \frac{1}{8 ^{\frac{1}{3 3}}}

True

, x = 8^{\frac{1}{3 3}}

True

The solutions are

x = 1, x = \frac{1}{8 ^{\frac{1}{3 3}}}, x = 8^{\frac{1}{3 3}}

y, x = lo g_{2} (2 y)

80 = 20 lo g_{10} (x)

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

ln (x) = 1 + 3 ln (2)

90 = 10 lo g_{10} (x \cdot 1 0^{12})

What is the answer to (log_{2}(x))^3=log_{8}(x) ?
The answer to (log_{2}(x))^3=log_{8}(x) is x=1,x= 1/(8^{\frac{1){3sqrt(3)}}},x=8^{1/(3sqrt(3))}
Solve for x: (log_{2}(x))^3=log_{8}(x)
The solution is x=1,x= 1/(8^{\frac{1){3sqrt(3)}}},x=8^{1/(3sqrt(3))}