What is the answer to log_{x-1}(6x-14)=2 ?

The answer to log_{x-1}(6x-14)=2 is x=5,x=3

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log_{x-1}(6x-14)=2

lo g_{x - 1} (6 x - 14) = 2

x = 5, x = 3

Solution steps

lo g_{x - 1} (6 x - 14) = 2

Apply log rules

\frac{ln ( 6 x - 14 )}{ln ( x - 1 )} = 2

Multiply both sides by

ln (x - 1)

\frac{ln ( 6 x - 14 )}{ln ( x - 1 )} ln (x - 1) = 2 ln (x - 1)

Simplify

ln (6 x - 14) = 2 ln (x - 1)

Apply log rules

6 x - 14 = (x - 1)^{2}

Solve

6 x - 14 = (x - 1)^{2} : x = 5, x = 3

x = 5, x = 3

Verify Solutions:

x = 5

True

, x = 3

True

The solutions are

x = 5, x = 3

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

ln (x - 4) + ln (x + 1) = ln (x - 8)

lo g_{3} (x^{2}) = - 2

- 26 + lo g_{4} ((4 - x)^{7}) = 9

lo g_{10} (10 c) = 2

What is the answer to log_{x-1}(6x-14)=2 ?
The answer to log_{x-1}(6x-14)=2 is x=5,x=3
Solve for x: log_{x-1}(6x-14)=2
The solution is x=5,x=3