What is the answer to 2log_{4}(x)+3log_{x}(4)=7 ?

The answer to 2log_{4}(x)+3log_{x}(4)=7 is x=64,x=2

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2log_{4}(x)+3log_{x}(4)=7

2 lo g_{4} (x) + 3 lo g_{x} (4) = 7

x = 64, x = 2

Solution steps

2 lo g_{4} (x) + 3 lo g_{x} (4) = 7

Apply log rules

2 lo g_{4} (x) + \frac{3}{lo g _{4} ( x )} = 7

Rewrite the equation with

lo g_{4} (x) = u

2 u + \frac{3}{u} = 7

Solve

2 u + \frac{3}{u} = 7 : u = 3, u = \frac{1}{2}

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

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 3 : x = 64

Solve

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

x = 64, x = 2

Verify Solutions:

x = 64

True

, x = 2

True

The solutions are

x = 64, x = 2

ln (x) + ln (x - 7) = 0

lo g_{3} (x) = 9

lo g_{x} (256) = 8

ln (x - 2) = 2 + 3 ln (2)

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

What is the answer to 2log_{4}(x)+3log_{x}(4)=7 ?
The answer to 2log_{4}(x)+3log_{x}(4)=7 is x=64,x=2
Solve for x: 2log_{4}(x)+3log_{x}(4)=7
The solution is x=64,x=2