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

The answer to log_{10}(x+2)-log_{10}(x-1)=4 is x= 3334/3333

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

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

x = \frac{3334}{3333}

Decimal

x = 1.00030 \dots

Solution steps

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

Add

lo g_{10} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 2 = 10000 (x - 1)

Solve

x + 2 = 10000 (x - 1) : x = \frac{3334}{3333}

x = \frac{3334}{3333}

Verify Solutions:

x = \frac{3334}{3333}

True

The solution is

x = \frac{3334}{3333}

x^{1 + l o g_{10} (x)} = 10 x

(lo g_{10} (x))^{2} = lo g_{10} (x^{2})

2 lo g_{10} (x) - lo g_{10} (x + 6) = 0

ln (\frac{1}{x}) + ln (2 x^{3}) = ln^{3} (x)

2 lo g_{10} (x) + 1 = lo g_{250} (x)

What is the answer to log_{10}(x+2)-log_{10}(x-1)=4 ?
The answer to log_{10}(x+2)-log_{10}(x-1)=4 is x= 3334/3333
Solve for x: log_{10}(x+2)-log_{10}(x-1)=4
The solution is x= 3334/3333