What is the answer to log_{10}(2x-3)=log_{10}(x-4)+1 ?

The answer to log_{10}(2x-3)=log_{10}(x-4)+1 is x= 37/8

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log_{10}(2x-3)=log_{10}(x-4)+1

lo g_{10} (2 x - 3) = lo g_{10} (x - 4) + 1

x = \frac{37}{8}

Decimal

x = 4.625

Solution steps

lo g_{10} (2 x - 3) = lo g_{10} (x - 4) + 1

Apply log rules

2 x - 3 = (x - 4) \cdot 10

Solve

2 x - 3 = (x - 4) \cdot 10 : x = \frac{37}{8}

x = \frac{37}{8}

Verify Solutions:

x = \frac{37}{8}

True

The solution is

x = \frac{37}{8}

lo g_{2} (4 + 2^{x}) = 5 - x

lo g_{x} (27) = - 0.5

ln (e^{x} + 1) = x

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

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

What is the answer to log_{10}(2x-3)=log_{10}(x-4)+1 ?
The answer to log_{10}(2x-3)=log_{10}(x-4)+1 is x= 37/8
Solve for x: log_{10}(2x-3)=log_{10}(x-4)+1
The solution is x= 37/8