What is the answer to log_{4}((n+3)^4)=4 ?

The answer to log_{4}((n+3)^4)=4 is n=1,n=-7

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log_{4}((n+3)^4)=4

lo g_{4} ((n + 3)^{4}) = 4

n = 1, n = - 7

Solution steps

lo g_{4} ((n + 3)^{4}) = 4

Apply exponent rule:

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

(n + 3)^{4} = ((n + 3)^{2})^{2}

lo g_{4} (((n + 3)^{2})^{2}) = 4

Apply log rules

(n + 3)^{2} = 16

Solve

(n + 3)^{2} = 16 : n = 1, n = - 7

n = 1, n = - 7

Verify Solutions:

n = 1

True

, n = - 7

True

The solutions are

n = 1, n = - 7

lo g_{9} (2 x - 3) = \frac{1}{2}

y, ln (x) \cdot y - 1 = 0

ln (x^{2}) + ln (x^{3}) + ln (x^{5}) = 10

lo g_{- 2 x - 3} (3 x^{2} + 2 x - 15) = 2

lo g_{\frac{1}{2}} (7 - 8 x) = - 2

What is the answer to log_{4}((n+3)^4)=4 ?
The answer to log_{4}((n+3)^4)=4 is n=1,n=-7
Solve for n: log_{4}((n+3)^4)=4
The solution is n=1,n=-7