What is the answer to x^{0.5log_{10}(x)}=0.01x^2 ?

The answer to x^{0.5log_{10}(x)}=0.01x^2 is x=10^{2+sqrt(1.0E-15)},x=10^{2-sqrt(1.0E-15)}

Solve for x: x^{0.5log_{10}(x)}=0.01x^2

The solution is x=10^{2+sqrt(1.0E-15)},x=10^{2-sqrt(1.0E-15)}

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x^{0.5 l o g_{10} (x)} = 0.01 x^{2}

x = 1 0^{2 + 1.0 E - 15}, x = 1 0^{2 - 1.0 E - 15}

Decimal Notation

x = 100.00000 \dots, x = 99.99999 \dots

Solution steps

x^{0.5 l o g_{10} (x)} = 0.01 x^{2}

Apply log rules

0.5 lo g_{10} (x) lo g_{10} (x) = lo g_{10} (0.01) + 2 lo g_{10} (x)

Rewrite the equation with

lo g_{10} (x) = u

0.5 uu = lo g_{10} (0.01) + 2 u

Solve

0.5 uu = lo g_{10} (0.01) + 2 u : u = 2 + 1.0 E - 15, u = 2 - 1.0 E - 15

u = 2 + 1.0 E - 15, u = 2 - 1.0 E - 15

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 2 + 1.0 E - 15 : x = 1 0^{2 + 1.0 E - 15}

Solve

lo g_{10} (x) = 2 - 1.0 E - 15 : x = 1 0^{2 - 1.0 E - 15}

x = 1 0^{2 + 1.0 E - 15}, x = 1 0^{2 - 1.0 E - 15}

Verify Solutions:

x = 1 0^{2 + 1.0 E - 15}

True

, x = 1 0^{2 - 1.0 E - 15}

True

The solutions are

x = 1 0^{2 + 1.0 E - 15}, x = 1 0^{2 - 1.0 E - 15}

x, z = ln (2 x + 3 y)

ln (3 x - 4) = 2.3

- lo g_{10} (x) = 4.7

lo g_{5} (x^{2} - 7 x + 7) = 0

lo g_{10} (4 x - 3) + lo g_{10} (x) = 0

What is the answer to x^{0.5log_{10}(x)}=0.01x^2 ?
The answer to x^{0.5log_{10}(x)}=0.01x^2 is x=10^{2+sqrt(1.0E-15)},x=10^{2-sqrt(1.0E-15)}
Solve for x: x^{0.5log_{10}(x)}=0.01x^2
The solution is x=10^{2+sqrt(1.0E-15)},x=10^{2-sqrt(1.0E-15)}