What is the answer to log_{7}(x^4)=2 ?

The answer to log_{7}(x^4)=2 is x=sqrt(7),x=-sqrt(7)

Solve for x: log_{7}(x^4)=2

The solution is x=sqrt(7),x=-sqrt(7)

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lo g_{7} (x^{4}) = 2

x = 7, x = - 7

Decimal

x = 2.64575 \dots, x = - 2.64575 \dots

Solution steps

lo g_{7} (x^{4}) = 2

Apply exponent rule:

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

x^{4} = (x^{2})^{2}

lo g_{7} ((x^{2})^{2}) = 2

Apply log rules

x^{2} = 7

Solve

x^{2} = 7 : x = 7, x = - 7

x = 7, x = - 7

Verify Solutions:

x = 7

True

, x = - 7

True

The solutions are

x = 7, x = - 7

ln (x^{2}) + 1 = 0

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

lo g_{5} (2 x + 3) = 3

lo g_{3} (2 x - 5) = 3

lo g_{\frac{1}{7}} (2 x + 5) = - 2

What is the answer to log_{7}(x^4)=2 ?
The answer to log_{7}(x^4)=2 is x=sqrt(7),x=-sqrt(7)
Solve for x: log_{7}(x^4)=2
The solution is x=sqrt(7),x=-sqrt(7)