What is the answer to log_{5}(3)+log_{5}(x+2)=2 ?

The answer to log_{5}(3)+log_{5}(x+2)=2 is x= 19/3

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log_{5}(3)+log_{5}(x+2)=2

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

x = \frac{19}{3}

Solution steps

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

Move

lo g_{5} (3)

to the right side

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

Apply log rules

x + 2 = \frac{25}{3}

Solve

x + 2 = \frac{25}{3} : x = \frac{19}{3}

x = \frac{19}{3}

Verify Solutions:

x = \frac{19}{3}

True

The solution is

x = \frac{19}{3}

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

ln (e^{2 x} + 3) = 2 x + ln (3)

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

lo g_{a} (32) = - \frac{5}{2}

3.5 = - lo g_{10} (c)

What is the answer to log_{5}(3)+log_{5}(x+2)=2 ?
The answer to log_{5}(3)+log_{5}(x+2)=2 is x= 19/3
Solve for x: log_{5}(3)+log_{5}(x+2)=2
The solution is x= 19/3