What is the answer to log_{10}(x^2+3)=log_{10}(x+6) ?

The answer to log_{10}(x^2+3)=log_{10}(x+6) is x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2

Solve for x: log_{10}(x^2+3)=log_{10}(x+6)

The solution is x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2

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lo g_{10} (x^{2} + 3) = lo g_{10} (x + 6)

x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

Decimal Notation

x = 2.30277 \dots, x = - 1.30277 \dots

Solution steps

lo g_{10} (x^{2} + 3) = lo g_{10} (x + 6)

Apply log rules

x^{2} + 3 = x + 6

Solve

x^{2} + 3 = x + 6 : x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

Verify Solutions:

x = \frac{1 + 13}{2}

True

, x = \frac{1 - 13}{2}

True

The solutions are

x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

a, lo g_{2} (a^{3}) + lo g_{2} (b) = 8

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

2 lo g_{10} (x) = 4

lo g_{3} ((x + 2)^{2}) + 1 = 7

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

What is the answer to log_{10}(x^2+3)=log_{10}(x+6) ?
The answer to log_{10}(x^2+3)=log_{10}(x+6) is x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2
Solve for x: log_{10}(x^2+3)=log_{10}(x+6)
The solution is x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2