What is the answer to n*log_{10}(n)=n ?

The answer to n*log_{10}(n)=n is n=10

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n*log_{10}(n)=n

n \cdot lo g_{10} (n) = n

n = 10

Solution steps

n lo g_{10} (n) = n

Move

n

to the left side

n lo g_{10} (n) - n = 0

Factor

n lo g_{10} (n) - n : n (lo g_{10} (n) - 1)

n (lo g_{10} (n) - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

n = 0 or lo g_{10} (n) - 1 = 0

Solve

lo g_{10} (n) - 1 = 0 : n = 10

Verify Solutions:

n = 0

False

, n = 10

True

The solution is

n = 10

lo g_{10} (x) = 6.33

lo g_{10} (3 x^{2} - 2 x) = 0

lo g_{9} (x^{2} - x + 3) = 0.5

- 1 + ln (x + 3) = 0

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