What is the answer to log_{4}(x^2-25)=1+log_{4}(x-1) ?

The answer to log_{4}(x^2-25)=1+log_{4}(x-1) is x=7

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log_{4}(x^2-25)=1+log_{4}(x-1)

lo g_{4} (x^{2} - 25) = 1 + lo g_{4} (x - 1)

x = 7

Solution steps

lo g_{4} (x^{2} - 25) = 1 + lo g_{4} (x - 1)

Apply log rules

x^{2} - 25 = 4 (x - 1)

Solve

x^{2} - 25 = 4 (x - 1) : x = 7, x = - 3

x = 7, x = - 3

Verify Solutions:

x = 7

True

, x = - 3

False

The solution is

x = 7

lo g_{10} (7 x) = - 2

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

ln (2 x - 3) = 2

lo g_{10} (9 x) = - 2

lo g_{3} (2 x - 1) + lo g_{2} (4) = 5

What is the answer to log_{4}(x^2-25)=1+log_{4}(x-1) ?
The answer to log_{4}(x^2-25)=1+log_{4}(x-1) is x=7
Solve for x: log_{4}(x^2-25)=1+log_{4}(x-1)
The solution is x=7