What is the answer to log_{10}(x)-log_{10}(8-5x)=2 ?

The answer to log_{10}(x)-log_{10}(8-5x)=2 is x= 800/501

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log_{10}(x)-log_{10}(8-5x)=2

lo g_{10} (x) - lo g_{10} (8 - 5 x) = 2

x = \frac{800}{501}

Decimal Notation

x = 1.59680 \dots

Solution steps

lo g_{10} (x) - lo g_{10} (8 - 5 x) = 2

Add

lo g_{10} (8 - 5 x)

to both sides

lo g_{10} (x) - lo g_{10} (8 - 5 x) + lo g_{10} (8 - 5 x) = 2 + lo g_{10} (8 - 5 x)

Simplify

lo g_{10} (x) = 2 + lo g_{10} (8 - 5 x)

Apply log rules

x = 100 (8 - 5 x)

Solve

x = 100 (8 - 5 x) : x = \frac{800}{501}

x = \frac{800}{501}

Verify Solutions:

x = \frac{800}{501}

True

The solution is

x = \frac{800}{501}

- 1 = ln (3 x)

lo g_{2} (x + 1) + lo g_{2} (x - 5) = 4

x, ln (2 x) = 4

lo g_{3} (x) = lo g_{3} (12)

lo g_{10} (x) = 3.2614400000000 \dots

What is the answer to log_{10}(x)-log_{10}(8-5x)=2 ?
The answer to log_{10}(x)-log_{10}(8-5x)=2 is x= 800/501
Solve for x: log_{10}(x)-log_{10}(8-5x)=2
The solution is x= 800/501