What is the answer to log_{3}(2x+3)=5-log_{3}(x+6) ?

The answer to log_{3}(2x+3)=5-log_{3}(x+6) is x= 15/2

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log_{3}(2x+3)=5-log_{3}(x+6)

lo g_{3} (2 x + 3) = 5 - lo g_{3} (x + 6)

x = \frac{15}{2}

Solution steps

lo g_{3} (2 x + 3) = 5 - lo g_{3} (x + 6)

Add

lo g_{3} (x + 6)

to both sides

lo g_{3} (2 x + 3) + lo g_{3} (x + 6) = 5 - lo g_{3} (x + 6) + lo g_{3} (x + 6)

Simplify

lo g_{3} (2 x + 3) + lo g_{3} (x + 6) = 5

Apply log rules

(2 x + 3) (x + 6) = 243

Solve

(2 x + 3) (x + 6) = 243 : x = \frac{15}{2}, x = - 15

x = \frac{15}{2}, x = - 15

Verify Solutions:

x = \frac{15}{2}

True

, x = - 15

False

The solution is

x = \frac{15}{2}

10000 - 0 = 2000 ln (\frac{3}{m})

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

lo g_{2 - 3 k} (125) = 3

lo g_{2} (y + 2) - lo g_{2} (y - 2) = 1

4 ln (x + 6) = - 8

What is the answer to log_{3}(2x+3)=5-log_{3}(x+6) ?
The answer to log_{3}(2x+3)=5-log_{3}(x+6) is x= 15/2
Solve for x: log_{3}(2x+3)=5-log_{3}(x+6)
The solution is x= 15/2