What is the answer to log_{x}(4)+log_{2}(x)=3 ?

The answer to log_{x}(4)+log_{2}(x)=3 is x=4,x=2

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log_{x}(4)+log_{2}(x)=3

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

x = 4, x = 2

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

\frac{2}{u} + u = 3

Solve

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

u = 2, u = 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

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

Solve

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

x = 4, x = 2

Verify Solutions:

x = 4

True

, x = 2

True

The solutions are

x = 4, x = 2

lo g_{4} (x + 8) + lo g_{4} (x + 2) = 2

lo g_{e} (x) + lo g_{e} (7 x + 1) = 1

ln (8^{x^{2}}) = ln (9^{x})

4 ln (x) = 2 ln (16)

lo g_{x} (243) = \frac{5}{3}

What is the answer to log_{x}(4)+log_{2}(x)=3 ?
The answer to log_{x}(4)+log_{2}(x)=3 is x=4,x=2
Solve for x: log_{x}(4)+log_{2}(x)=3
The solution is x=4,x=2