What is the answer to (log_{10}(10x))2-4log_{10}(10x)-5=0 ?

The answer to (log_{10}(10x))2-4log_{10}(10x)-5=0 is x= 1/(1000sqrt(10))

Solve for x: (log_{10}(10x))2-4log_{10}(10x)-5=0

The solution is x= 1/(1000sqrt(10))

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(lo g_{10} (10 x)) 2 - 4 lo g_{10} (10 x) - 5 = 0

x = \frac{1}{1000 10}

Decimal Notation

x = 0.00031 \dots

Solution steps

(lo g_{10} (10 x)) \cdot 2 - 4 lo g_{10} (10 x) - 5 = 0

Add similar elements:

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

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

Move

5

to the right side

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

Divide both sides by

- 2

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

Apply log rules

10 x = \frac{1}{100 10}

Solve

10 x = \frac{1}{100 10} : x = \frac{1}{1000 10}

x = \frac{1}{1000 10}

Verify Solutions:

x = \frac{1}{1000 10}

True

The solution is

x = \frac{1}{1000 10}

6 lo g_{10} (a) + 6 lo g_{10} (a - 9) = 2

ln (x - 1) - ln (x + 2) = ln (2)

a lo g_{2} (3.5) = lo g_{27} (- lo g_{22} (x))

x - 7 + lo g_{2} (x + 8) = - 5

ln (2) - ln (3 x + 4) + ln (4 - 3 x) = ln (2)

What is the answer to (log_{10}(10x))2-4log_{10}(10x)-5=0 ?
The answer to (log_{10}(10x))2-4log_{10}(10x)-5=0 is x= 1/(1000sqrt(10))
Solve for x: (log_{10}(10x))2-4log_{10}(10x)-5=0
The solution is x= 1/(1000sqrt(10))