What is the answer to 2log_{5}(x)=3-log_{x}(5) ?

The answer to 2log_{5}(x)=3-log_{x}(5) is x=5,x=sqrt(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2log_{5}(x)=3-log_{x}(5)

2 lo g_{5} (x) = 3 - lo g_{x} (5)

x = 5, x = 5

Decimal Notation

x = 5, x = 2.23606 \dots

Solution steps

2 lo g_{5} (x) = 3 - lo g_{x} (5)

Apply log rules

2 lo g_{5} (x) = 3 - \frac{1}{lo g _{5} ( x )}

Rewrite the equation with

lo g_{5} (x) = u

2 u = 3 - \frac{1}{u}

Solve

2 u = 3 - \frac{1}{u} : u = 1, u = \frac{1}{2}

u = 1, u = \frac{1}{2}

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 1 : x = 5

Solve

lo g_{5} (x) = \frac{1}{2} : x = 5

x = 5, x = 5

Verify Solutions:

x = 5

True

, x = 5

True

The solutions are

x = 5, x = 5

x, y^{5} = ln (x y)

200 = 93 lo g_{10} (d) + 65

lo g_{10} (x) = 3855173601

lo g_{3} (9) = lo g_{3} (x)

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

What is the answer to 2log_{5}(x)=3-log_{x}(5) ?
The answer to 2log_{5}(x)=3-log_{x}(5) is x=5,x=sqrt(5)
Solve for x: 2log_{5}(x)=3-log_{x}(5)
The solution is x=5,x=sqrt(5)