What is the answer to log_{10}(x-1)=2log_{10}(x)-1 ?

The answer to log_{10}(x-1)=2log_{10}(x)-1 is x=5+sqrt(15),x=5-sqrt(15)

Solve for x: log_{10}(x-1)=2log_{10}(x)-1

The solution is x=5+sqrt(15),x=5-sqrt(15)

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

x = 5 + 15, x = 5 - 15

Decimal Notation

x = 8.87298 \dots, x = 1.12701 \dots

Solution steps

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

Apply log rules

(x - 1) \cdot 10 = x^{2}

Solve

(x - 1) \cdot 10 = x^{2} : x = 5 + 15, x = 5 - 15

x = 5 + 15, x = 5 - 15

Verify Solutions:

x = 5 + 15

True

, x = 5 - 15

True

The solutions are

x = 5 + 15, x = 5 - 15

3 lo g_{e} (t) = 5

lo g_{10} (3 x^{3}) = 8

2 lo g_{2} (x - 3) - lo g_{2} (x + 6) = 0

ln (x + 3) \cdot ln (x - 3) = 0

lo g_{10} (5 x + 3) = lo g_{10} (12)

What is the answer to log_{10}(x-1)=2log_{10}(x)-1 ?
The answer to log_{10}(x-1)=2log_{10}(x)-1 is x=5+sqrt(15),x=5-sqrt(15)
Solve for x: log_{10}(x-1)=2log_{10}(x)-1
The solution is x=5+sqrt(15),x=5-sqrt(15)