What is the answer to log_{10}(x)+log_{10}(x-7)=2 ?

The answer to log_{10}(x)+log_{10}(x-7)=2 is x=(7+sqrt(449))/2

Solve for x: log_{10}(x)+log_{10}(x-7)=2

The solution is x=(7+sqrt(449))/2

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lo g_{10} (x) + lo g_{10} (x - 7) = 2

x = \frac{7 + 449}{2}

Decimal Notation

x = 14.09481 \dots

Solution steps

lo g_{10} (x) + lo g_{10} (x - 7) = 2

Apply log rules

x (x - 7) = 100

Solve

x (x - 7) = 100 : x = \frac{7 + 449}{2}, x = \frac{7 - 449}{2}

x = \frac{7 + 449}{2}, x = \frac{7 - 449}{2}

Verify Solutions:

x = \frac{7 + 449}{2}

True

, x = \frac{7 - 449}{2}

False

The solution is

x = \frac{7 + 449}{2}

lo g_{2} (x) + lo g_{4} (x) = 3

lo g_{5} (2 x - 3) = 2

lo g_{2} (x + 4) = 2 - lo g_{2} (x + 7)

lo g_{2} (x + 3) = 5

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

What is the answer to log_{10}(x)+log_{10}(x-7)=2 ?
The answer to log_{10}(x)+log_{10}(x-7)=2 is x=(7+sqrt(449))/2
Solve for x: log_{10}(x)+log_{10}(x-7)=2
The solution is x=(7+sqrt(449))/2