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

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

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

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

x = \frac{15}{2}

Decimal Notation

x = 7.5

Solution steps

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

Move

lo g_{3} (2)

to the right side

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

Apply log rules

x - 3 = \frac{9}{2}

Solve

x - 3 = \frac{9}{2} : x = \frac{15}{2}

x = \frac{15}{2}

Verify Solutions:

x = \frac{15}{2}

True

The solution is

x = \frac{15}{2}

x, 2 ln (x) + 1 = 0

ln (x) = 8.536595743

x = x ln (x)

ln (4 x - 1) = 2

lo g_{4} (4 x) - lo g_{4} (x - 6) = 2

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