What is the answer to log_{10}(x^5)=(log_{10}(x^5))^3 ?

The answer to log_{10}(x^5)=(log_{10}(x^5))^3 is x=1,x= 1/(\sqrt[5]{10)},x=\sqrt[5]{10}

Solve for x: log_{10}(x^5)=(log_{10}(x^5))^3

The solution is x=1,x= 1/(\sqrt[5]{10)},x=\sqrt[5]{10}

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lo g_{10} (x^{5}) = (lo g_{10} (x^{5}))^{3}

x = 1, x = \frac{1}{5 10}, x = 510

Decimal

x = 1, x = 0.63095 \dots, x = 1.58489 \dots

Solution steps

lo g_{10} (x^{5}) = (lo g_{10} (x^{5}))^{3}

Rewrite the equation with

lo g_{10} (x^{5}) = u

u = (u)^{3}

Solve

u = u^{3} : u = 0, u = - 1, u = 1

u = 0, u = - 1, u = 1

Substitute back

u = lo g_{10} (x^{5}),

solve for

x

Solve

lo g_{10} (x^{5}) = 0 : x = 1

Solve

lo g_{10} (x^{5}) = - 1 : x = \frac{1}{5 10}

Solve

lo g_{10} (x^{5}) = 1 : x = 510

x = 1, x = \frac{1}{5 10}, x = 510

Verify Solutions:

x = 1

True

, x = \frac{1}{5 10}

True

, x = 510

True

The solutions are

x = 1, x = \frac{1}{5 10}, x = 510

lo g_{10} (- 2 x) + lo g_{10} (6) = 1

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

lo g_{x} (512) = \frac{3}{2}

y, lo g_{x} (y) = 2

ln (4) - ln (3) = 2 ln (x) - ln (x + 1)

What is the answer to log_{10}(x^5)=(log_{10}(x^5))^3 ?
The answer to log_{10}(x^5)=(log_{10}(x^5))^3 is x=1,x= 1/(\sqrt[5]{10)},x=\sqrt[5]{10}
Solve for x: log_{10}(x^5)=(log_{10}(x^5))^3
The solution is x=1,x= 1/(\sqrt[5]{10)},x=\sqrt[5]{10}