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

The answer to log_{10}(y^{10})=2 is y=10^{1/5},y=-10^{1/5}

Solve for y: log_{10}(y^{10})=2

The solution is y=10^{1/5},y=-10^{1/5}

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

y = 1 0^{\frac{1}{5}}, y = - 1 0^{\frac{1}{5}}

Decimal Notation

y = 1.58489 \dots, y = - 1.58489 \dots

Solution steps

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

Apply exponent rule:

a^{2 \cdot n} = (a^{2})^{n}

y^{10} = (y^{2})^{5}

lo g_{10} ((y^{2})^{5}) = 2

Apply log rules

y^{2} = 1 0^{\frac{2}{5}}

Solve

y^{2} = 1 0^{\frac{2}{5}} : y = 1 0^{\frac{1}{5}}, y = - 1 0^{\frac{1}{5}}

y = 1 0^{\frac{1}{5}}, y = - 1 0^{\frac{1}{5}}

Verify Solutions:

y = 1 0^{\frac{1}{5}}

True

, y = - 1 0^{\frac{1}{5}}

True

The solutions are

y = 1 0^{\frac{1}{5}}, y = - 1 0^{\frac{1}{5}}

2 lo g_{10} (x) + 1 = 5

2 lo g_{2} (x) = 4

(ln (x))^{2} = 10 - 9 ln (x)

ln (x + 9) + ln (x - 5) = 2 ln (x)

x ln (x) = 6 ln (x)

What is the answer to log_{10}(y^{10})=2 ?
The answer to log_{10}(y^{10})=2 is y=10^{1/5},y=-10^{1/5}
Solve for y: log_{10}(y^{10})=2
The solution is y=10^{1/5},y=-10^{1/5}