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

The answer to 2log_{10}(x-1)=2+2log_{x}(x) is x=101

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2log_{10}(x-1)=2+2log_{x}(x)

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

x = 101

Solution steps

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

Divide both sides by

2

\frac{2 lo g _{10} ( x - 1 )}{2} = \frac{2}{2} + \frac{2 lo g _{x} ( x )}{2}

Simplify

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

Apply log rules

x - 1 = 100

Solve

x - 1 = 100 : x = 101

x = 101

Verify Solutions:

x = 101

True

The solution is

x = 101

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

2 lo g_{10} (3 - x) = 1 - x

lo g_{2} (4 x + 9) = 4

lo g_{2} (x) + lo g_{8} (x) = 8

lo g_{7} (7 x - 3) = lo g_{7} (5 x + 15)

What is the answer to 2log_{10}(x-1)=2+2log_{x}(x) ?
The answer to 2log_{10}(x-1)=2+2log_{x}(x) is x=101
Solve for x: 2log_{10}(x-1)=2+2log_{x}(x)
The solution is x=101