What is the answer to x^{log_{10}(x)}=10^6x ?

The answer to x^{log_{10}(x)}=10^6x is x=1000,x= 1/100

Solve for x: x^{log_{10}(x)}=10^6x

The solution is x=1000,x= 1/100

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x^{l o g_{10} (x)} = 1 0^{6} x

x = 1000, x = \frac{1}{100}

Solution steps

x^{l o g_{10} (x)} = 1 0^{6} x

Apply log rules

lo g_{10} (x) lo g_{10} (x) = lo g_{10} (x) + 6

Rewrite the equation with

lo g_{10} (x) = u

uu = u + 6

Solve

uu = u + 6 : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 3 : x = 1000

Solve

lo g_{10} (x) = - 2 : x = \frac{1}{100}

x = 1000, x = \frac{1}{100}

Verify Solutions:

x = 1000

True

, x = \frac{1}{100}

True

The solutions are

x = 1000, x = \frac{1}{100}

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

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

lo g_{4} (X) = 0

- 1 = - lo g_{\frac{1}{2}} (x + 3) - 2

lo g_{8} (3 x + 1) = 2

What is the answer to x^{log_{10}(x)}=10^6x ?
The answer to x^{log_{10}(x)}=10^6x is x=1000,x= 1/100
Solve for x: x^{log_{10}(x)}=10^6x
The solution is x=1000,x= 1/100