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

The answer to log_{10}(x)-log_{10}(2-3x)=1 is x= 20/31

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

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

x = \frac{20}{31}

Decimal Notation

x = 0.64516 \dots

Solution steps

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

Add

lo g_{10} (2 - 3 x)

to both sides

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

Simplify

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

Apply log rules

x = 10 (2 - 3 x)

Solve

x = 10 (2 - 3 x) : x = \frac{20}{31}

x = \frac{20}{31}

Verify Solutions:

x = \frac{20}{31}

True

The solution is

x = \frac{20}{31}

5 - 4 lo g_{3} (x) = lo g_{x} (3)

0.59 = lo g_{10} (x)

lo g_{x} (8) = 6

lo g_{x} (8) = 2

ln (5 x + 1) + ln (3 x - 1) = ln (8 x - 3)

What is the answer to log_{10}(x)-log_{10}(2-3x)=1 ?
The answer to log_{10}(x)-log_{10}(2-3x)=1 is x= 20/31
Solve for x: log_{10}(x)-log_{10}(2-3x)=1
The solution is x= 20/31