What is the answer to log_{2}(x)+log_{x}(2)=2.5 ?

The answer to log_{2}(x)+log_{x}(2)=2.5 is x=4,x=sqrt(2)

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log_{2}(x)+log_{x}(2)=2.5

lo g_{2} (x) + lo g_{x} (2) = 2.5

x = 4, x = 2

Decimal Notation

x = 4, x = 1.41421 \dots

Solution steps

lo g_{2} (x) + lo g_{x} (2) = 2.5

Apply log rules

lo g_{2} (x) + \frac{1}{lo g _{2} ( x )} = 2.5

Rewrite the equation with

lo g_{2} (x) = u

u + \frac{1}{u} = 2.5

Solve

u + \frac{1}{u} = 2.5 : u = 2, u = \frac{1}{2}

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

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 2 : x = 4

Solve

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

x = 4, x = 2

Verify Solutions:

x = 4

True

, x = 2

True

The solutions are

x = 4, x = 2

lo g_{5} (2 x + 23) = lo g_{5} (x - 5)

lo g_{5} (x^{2} - 9 x + 15) = 2

- 8.66 ln (x) + 8.66 ln (0.6) + 15 = 0

lo g_{16} (3 x) = lo g_{16} (x + 10)

0 = ln (x) + 3

What is the answer to log_{2}(x)+log_{x}(2)=2.5 ?
The answer to log_{2}(x)+log_{x}(2)=2.5 is x=4,x=sqrt(2)
Solve for x: log_{2}(x)+log_{x}(2)=2.5
The solution is x=4,x=sqrt(2)