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

The answer to log_{10}(x+1)+log_{10}(2)=log_{10}(5x) is x= 2/3

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log_{10}(x+1)+log_{10}(2)=log_{10}(5x)

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

x = \frac{2}{3}

Decimal

x = 0.66666 \dots

Solution steps

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

Apply log rules

(x + 1) \cdot 2 = 5 x

Solve

(x + 1) \cdot 2 = 5 x : x = \frac{2}{3}

x = \frac{2}{3}

Verify Solutions:

x = \frac{2}{3}

True

The solution is

x = \frac{2}{3}

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

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

ln (x) = ln (3 x + 1) + 1

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

4 ln (3 x + 5) - 12 = 16

What is the answer to log_{10}(x+1)+log_{10}(2)=log_{10}(5x) ?
The answer to log_{10}(x+1)+log_{10}(2)=log_{10}(5x) is x= 2/3
Solve for x: log_{10}(x+1)+log_{10}(2)=log_{10}(5x)
The solution is x= 2/3