What is the answer to log_{10}(x)(2x)=5x ?

The answer to log_{10}(x)(2x)=5x is x=100sqrt(10)

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log_{10}(x)(2x)=5x

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

x = 10010

Decimal Notation

x = 316.22776 \dots

Solution steps

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

Move

5 x

to the left side

lo g_{10} (x) \cdot 2 x - 5 x = 0

Factor

lo g_{10} (x) \cdot 2 x - 5 x : x (2 lo g_{10} (x) - 5)

x (2 lo g_{10} (x) - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 lo g_{10} (x) - 5 = 0

Solve

2 lo g_{10} (x) - 5 = 0 : x = 10010

Verify Solutions:

x = 0

False

, x = 10010

True

The solution is

x = 10010

7.35 = 7.2 + lo g_{10} (x)

- 4 = lo g_{10} (x)

lo g_{a} (X) = 2

lo g_{a} (X) = 0

lo g_{10} (x - 2) = lo g_{10} (27)

What is the answer to log_{10}(x)(2x)=5x ?
The answer to log_{10}(x)(2x)=5x is x=100sqrt(10)
Solve for x: log_{10}(x)(2x)=5x
The solution is x=100sqrt(10)