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

The answer to x^2log_{10}(x)=10x^2 is x=10^{10}

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

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

x = 1 0^{10}

Decimal Notation

x = 10000000000

Solution steps

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

Move

10 x^{2}

to the left side

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

Factor

x^{2} lo g_{10} (x) - 10 x^{2} : x^{2} (lo g_{10} (x) - 10)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Verify Solutions:

x = 0

False

, x = 1 0^{10}

True

The solution is

x = 1 0^{10}

lo g_{6} (x + 7) - lo g_{6} (x) = 2

lo g_{10} (x + 1) = lo g_{10} (x - 1) + 3

lo g_{2} (4 x - 6) = 1

lo g_{10} (x) = 2

ln (x) = 0

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