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

The answer to log_{5}(3x)+3log_{5}(2)=3 is x= 125/24

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

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

x = \frac{125}{24}

Decimal Notation

x = 5.20833 \dots

Solution steps

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

Move

3 lo g_{5} (2)

to the right side

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

Apply log rules

3 x = \frac{125}{8}

Solve

3 x = \frac{125}{8} : x = \frac{125}{24}

x = \frac{125}{24}

Verify Solutions:

x = \frac{125}{24}

True

The solution is

x = \frac{125}{24}

- lo g_{10} (x) = 13.5

x, y^{3} = ln (x y)

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

lo g_{e} (x - 4) = 5

lo g_{2} (9) = 2 lo g_{2} (x)

What is the answer to log_{5}(3x)+3log_{5}(2)=3 ?
The answer to log_{5}(3x)+3log_{5}(2)=3 is x= 125/24
Solve for x: log_{5}(3x)+3log_{5}(2)=3
The solution is x= 125/24