Question

If 6^(n + 5) - 6^(n + 3) = 7560, What is the value of n?

Answer 1

$6^{n + 5} - 6^{n + 3} = 7560$

$\text{Factor the expression}$

☛ $(6^2 - 1) \times 6^{n + 3} = 7560$

$\text{Evaluate the power}$

☛ $(36 - 1) \times 6^{n + 3} = 7560$

$\text{Subtract the numbers}$

☛ $35 \times 6^{n + 3} = 7560$

$\text{Divide both the sides by 35}$

☛ $6^{n + 3} = 216$

$\text{Write in exponential form}$

☛ $6^{n + 3} = 6^3$

$\text{Set the exponents equal}$

☛ $n + 3 = 3$

$\text{Move the terms}$

☛ $n = 3 - 3$

$\text{Calculate}$

☛ $n = 0$


∴ $\pink{\underline{\pink{\underline{\tt{\red{The\:value\:of\:n\:is\:0}}}}}}$

Answer 2

Answer:

0

Step By Step Explanation:

$\mathsf{ {6}^{(n \: + \: 5)} - {6}^{(n \: + \: 3)} = 7560}$

$\mathsf { ⇒{6}^{n} \times {6}^{5} - {6}^{n} \times {6}^{3} = 7560}$

$\mathsf { ⇒ {6}^{n} ( {6}^{5} - {6}^{3} )= 7560}$

$\mathsf{ ⇒ {6}^{n} (7776 - 216) = 7560}$

$\mathsf{⇒ {6}^{n} = \frac{7560}{7560} }$

$\mathsf{⇒ {6}^{n} = {6}^{0} }$

$\therefore{ \mathsf{n = 0}}$

Hence, The Required value of n is 0.