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

The answer to log_{10}(3x)+log_{10}(3)=2 is x= 100/9

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log_{10}(3x)+log_{10}(3)=2

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

x = \frac{100}{9}

Decimal Notation

x = 11.11111 \dots

Solution steps

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

Move

lo g_{10} (3)

to the right side

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

Apply log rules

3 x = \frac{100}{3}

Solve

3 x = \frac{100}{3} : x = \frac{100}{9}

x = \frac{100}{9}

Verify Solutions:

x = \frac{100}{9}

True

The solution is

x = \frac{100}{9}

lo g_{2} (x - 2) = 0

2 lo g_{10} (3 x) = 4

lo g_{9} (a) = 4

0.28 = ln (y)

lo g_{2} (x^{2} + 2 x - 3) = 0

What is the answer to log_{10}(3x)+log_{10}(3)=2 ?
The answer to log_{10}(3x)+log_{10}(3)=2 is x= 100/9
Solve for x: log_{10}(3x)+log_{10}(3)=2
The solution is x= 100/9