What is the answer to 4log_{4}(x)=9log_{x}(4) ?

The answer to 4log_{4}(x)=9log_{x}(4) is x=8,x= 1/8

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4log_{4}(x)=9log_{x}(4)

4 lo g_{4} (x) = 9 lo g_{x} (4)

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

Solution steps

4 lo g_{4} (x) = 9 lo g_{x} (4)

Apply log rules

4 lo g_{4} (x) = \frac{9}{lo g _{4} ( x )}

Rewrite the equation with

lo g_{4} (x) = u

4 u = \frac{9}{u}

Solve

4 u = \frac{9}{u} : u = \frac{3}{2}, u = - \frac{3}{2}

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

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = \frac{3}{2} : x = 8

Solve

lo g_{4} (x) = - \frac{3}{2} : x = \frac{1}{8}

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

Verify Solutions:

x = 8

True

, x = \frac{1}{8}

True

The solutions are

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

2 lo g_{10} (x + 1) = x - 1

lo g_{2} (5 + 2 x) - lo g_{2} (4 - x) = 3

ln (x) = ln (5) + ln (x - 1)

lo g_{4} (\frac{3 - x}{7}) = 1

8 lo g_{9} (2) = lo g_{9} (x)

What is the answer to 4log_{4}(x)=9log_{x}(4) ?
The answer to 4log_{4}(x)=9log_{x}(4) is x=8,x= 1/8
Solve for x: 4log_{4}(x)=9log_{x}(4)
The solution is x=8,x= 1/8