What is the answer to log_{10}(5x-1)=2log_{10}(x-2) ?

The answer to log_{10}(5x-1)=2log_{10}(x-2) is x=(9+sqrt(61))/2

Solve for x: log_{10}(5x-1)=2log_{10}(x-2)

The solution is x=(9+sqrt(61))/2

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lo g_{10} (5 x - 1) = 2 lo g_{10} (x - 2)

x = \frac{9 + 61}{2}

Decimal

x = 8.40512 \dots

Solution steps

lo g_{10} (5 x - 1) = 2 lo g_{10} (x - 2)

Apply log rules

5 x - 1 = (x - 2)^{2}

Solve

5 x - 1 = (x - 2)^{2} : x = \frac{9 + 61}{2}, x = \frac{9 - 61}{2}

x = \frac{9 + 61}{2}, x = \frac{9 - 61}{2}

Verify Solutions:

x = \frac{9 + 61}{2}

True

, x = \frac{9 - 61}{2}

False

The solution is

x = \frac{9 + 61}{2}

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

lo g_{7} (x^{2} - 3 x + 3) = 0

lo g_{3} (7 x - 15) = 3

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

lo g_{4} (\frac{X + 3}{4}) = - 1

What is the answer to log_{10}(5x-1)=2log_{10}(x-2) ?
The answer to log_{10}(5x-1)=2log_{10}(x-2) is x=(9+sqrt(61))/2
Solve for x: log_{10}(5x-1)=2log_{10}(x-2)
The solution is x=(9+sqrt(61))/2