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

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

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

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

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

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

Add

lo g_{10} (x)

to both sides

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

Simplify

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

Apply log rules

(3 x + 1) x = 10

Solve

(3 x + 1) x = 10 : x = \frac{5}{3}, x = - 2

x = \frac{5}{3}, x = - 2

Verify Solutions:

x = \frac{5}{3}

True

, x = - 2

False

The solution is

x = \frac{5}{3}

x, ln (x - 1) = ln (y + 3) + c

lo g_{3} (x - 8) - lo g_{3} (x) = 2

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

\frac{ln ( x )}{x} = 0.0975

lo g_{e} (x) + 4 = lo g_{e} (x + 6)

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