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

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

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

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

x = 4, x = 2

Decimal Notation

x = 4, x = 1.41421 \dots

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

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

Solve

\frac{1}{u} + 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_{x} (8) = 0.5

lo g_{x} (49) = lo g_{7} (343) - 1

9 = 10 lo g_{10} (x)

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

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

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