What is the answer to log_{7}(x-5)+log_{7}(3x-1)=2 ?

The answer to log_{7}(x-5)+log_{7}(3x-1)=2 is x= 22/3

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log_{7}(x-5)+log_{7}(3x-1)=2

lo g_{7} (x - 5) + lo g_{7} (3 x - 1) = 2

x = \frac{22}{3}

Decimal Notation

x = 7.33333 \dots

Solution steps

lo g_{7} (x - 5) + lo g_{7} (3 x - 1) = 2

Apply log rules

(x - 5) (3 x - 1) = 49

Solve

(x - 5) (3 x - 1) = 49 : x = \frac{22}{3}, x = - 2

x = \frac{22}{3}, x = - 2

Verify Solutions:

x = \frac{22}{3}

True

, x = - 2

False

The solution is

x = \frac{22}{3}

x - 2 x ln (x) = 0

ln (6 x + 2) = 2

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

ln (x) - ln (x - 2000) = 14876

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

What is the answer to log_{7}(x-5)+log_{7}(3x-1)=2 ?
The answer to log_{7}(x-5)+log_{7}(3x-1)=2 is x= 22/3
Solve for x: log_{7}(x-5)+log_{7}(3x-1)=2
The solution is x= 22/3