What is the answer to log_{3}((11x+30)^4)=16 ?

The answer to log_{3}((11x+30)^4)=16 is x= 51/11 ,x=-111/11

Solve for x: log_{3}((11x+30)^4)=16

The solution is x= 51/11 ,x=-111/11

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lo g_{3} ((11 x + 30)^{4}) = 16

x = \frac{51}{11}, x = - \frac{111}{11}

Decimal Notation

x = 4.63636 \dots, x = - 10.09090 \dots

Solution steps

lo g_{3} ((11 x + 30)^{4}) = 16

Apply exponent rule:

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

(11 x + 30)^{4} = ((11 x + 30)^{2})^{2}

lo g_{3} (((11 x + 30)^{2})^{2}) = 16

Apply log rules

(11 x + 30)^{2} = 6561

Solve

(11 x + 30)^{2} = 6561 : x = \frac{51}{11}, x = - \frac{111}{11}

x = \frac{51}{11}, x = - \frac{111}{11}

Verify Solutions:

x = \frac{51}{11}

True

, x = - \frac{111}{11}

True

The solutions are

x = \frac{51}{11}, x = - \frac{111}{11}

lo g_{23} (5 x - 1) = 2

2 lo g_{10} (5 x) = 6

2 ln (n) = ln (n^{2})

lo g_{2} (x + 8) = \frac{2}{21}

lo g_{3} (2 x) = 6 + 2 lo g_{3} (x)

What is the answer to log_{3}((11x+30)^4)=16 ?
The answer to log_{3}((11x+30)^4)=16 is x= 51/11 ,x=-111/11
Solve for x: log_{3}((11x+30)^4)=16
The solution is x= 51/11 ,x=-111/11