What is x>10log_{10}(x) ?

The solution to x>10log_{10}(x) is 0 10

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x>10log_{10}(x)

x > 10 lo g_{10} (x)

0 < x < - \frac{10 W _{0} ( - \frac{l n ( 10 )}{10} )}{ln ( 10 )} or x > 10

Interval Notation

0, - \frac{10 W _{0} ( - \frac{l n ( 10 )}{10} )}{ln ( 10 )} \cup (10, \infty)

Decimal Notation

0 < x < 1.37128 \dots or x > 10

Solution steps

x > 10 lo g_{10} (x)

Move

10 lo g_{10} (x)

to the left side

x - 10 lo g_{10} (x) > 0

Move

x

to the right side

- 10 lo g_{10} (x) > - x

Multiply both sides by

- 1

10 lo g_{10} (x) < x

Divide both sides by

10

lo g_{10} (x) < \frac{x}{10}

For a>1, if

f (x) < g (x),

then

a^{f (x)} < a^{g (x)}

a = 10

1 0^{l o g_{10} (x)} < 1 0^{\frac{x}{10}}

Simplify

1 0^{l o g_{10} (x)} : x

x < 1 0^{\frac{x}{10}}

Solve

x < 1 0^{\frac{x}{10}} : x < - \frac{10 W _{0} ( - \frac{l n ( 10 )}{10} )}{ln ( 10 )} or x > 10

Find positive values for logs:

x > 0

Combine the intervals

x < - \frac{10 W _{0} ( - \frac{l n ( 10 )}{10} )}{ln ( 10 )} or x > 10 and x > 0

Merge Overlapping Intervals

0 < x < - \frac{10 W _{0} ( - \frac{l n ( 10 )}{10} )}{ln ( 10 )} or x > 10

2 x^{3} - 18 x^{2} + 40 x

\frac{x + 17}{5} - \frac{3 x - 7}{4} = - 2

12 x + 3 = 11 x + 9

32 + 8 = a 2

t^{2} + 4 = 42 t

What is x>10log_{10}(x) ?
The solution to x>10log_{10}(x) is 0<x<-(10\W_{0}(-\frac{ln(10))/(10))}{ln(10)}\lor x>10