What is the answer to 2log_{4}(x-1)+log_{4}(x-1)=6 ?

The answer to 2log_{4}(x-1)+log_{4}(x-1)=6 is x=17

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2log_{4}(x-1)+log_{4}(x-1)=6

2 lo g_{4} (x - 1) + lo g_{4} (x - 1) = 6

x = 17

Solution steps

2 lo g_{4} (x - 1) + lo g_{4} (x - 1) = 6

Add similar elements:

2 lo g_{4} (x - 1) + lo g_{4} (x - 1) = 3 lo g_{4} (x - 1)

3 lo g_{4} (x - 1) = 6

Divide both sides by

3

lo g_{4} (x - 1) = 2

Apply log rules

x - 1 = 16

Solve

x - 1 = 16 : x = 17

x = 17

Verify Solutions:

x = 17

True

The solution is

x = 17

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

2 ln (x) = ln (6 - x) + ln (3)

lo g_{10} (x) = \frac{1}{2}

lo g_{x} (512) = 3

lo g_{x} (5) = \frac{1}{3}

What is the answer to 2log_{4}(x-1)+log_{4}(x-1)=6 ?
The answer to 2log_{4}(x-1)+log_{4}(x-1)=6 is x=17
Solve for x: 2log_{4}(x-1)+log_{4}(x-1)=6
The solution is x=17