What is the answer to log_{10}(4x+5)=1+log_{10}(x-1) ?

The answer to log_{10}(4x+5)=1+log_{10}(x-1) is x= 5/2

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log_{10}(4x+5)=1+log_{10}(x-1)

lo g_{10} (4 x + 5) = 1 + lo g_{10} (x - 1)

x = \frac{5}{2}

Decimal Notation

x = 2.5

Solution steps

lo g_{10} (4 x + 5) = 1 + lo g_{10} (x - 1)

Apply log rules

4 x + 5 = 10 (x - 1)

Solve

4 x + 5 = 10 (x - 1) : x = \frac{5}{2}

x = \frac{5}{2}

Verify Solutions:

x = \frac{5}{2}

True

The solution is

x = \frac{5}{2}

lo g_{2} (x + 2) = 5

lo g_{3} (x) = 5

ln (x) = \frac{1}{x}

lo g_{2} (3 - x) = lo g_{2} (2 x + 18)

lo g_{2} (8 x - 26) + lo g_{2} (4 x - 20) = 2

What is the answer to log_{10}(4x+5)=1+log_{10}(x-1) ?
The answer to log_{10}(4x+5)=1+log_{10}(x-1) is x= 5/2
Solve for x: log_{10}(4x+5)=1+log_{10}(x-1)
The solution is x= 5/2