Question

4) Solve : (16)2n+1 = (8)"-1
=
pls answer correctly ​

Answer 1

Question:

Solve : $\tt {(16)}^{2n+1} = {(8)}^{n-1}$

Solution :

$\tt {(16)}^{2n+1} = {(8)}^{n-1}$

$\tt \implies {({2}^{4})}^{2n+1} = {({2}^{3})}^{n-1}$

$\tt \implies {(2)}^{4(2n+1)} = {(2)}^{3(n-1)}$

$\tt \implies$ 4(2n+1) = 3(n-1)

$\tt \implies$ 8n + 4 = 3n - 3

$\tt \implies$ 8n - 3n = - 3 - 4

$\tt \implies$ 5n = - 7

$\tt \implies$ n = $\tt \frac{-7}{5}$

n = $\tt \frac{-7}{5}$

Properties of Indices :

● $\tt {a}^{b} × {a}^{c} = {a}^{b+c}$

● $\tt {a}^{b} ÷ {a}^{c} = {a}^{b-c}$

● $\tt {({a}^{b})}^{c} = {a}^{bc}$

● $\tt {a}^{1} = a$

● $\tt {a}^{0} = 1$

Answer 2

Answer:

Question:

Solve : $\sf {(16)}^{2n+1} = {(8)}^{n-1}$

Solution :

$\sf {(16)}^{2n+1} = {(8)}^{n-1}$

$\sf \implies {({2}^{4})}^{2n+1} = {({2}^{3})}^{n-1}$

$\sf \implies {(2)}^{4(2n+1)} = {(2)}^{3(n-1)}$

$\sf \implies$ 4(2n+1) = 3(n-1)

$\sf \implies$ 8n + 4 = 3n - 3

$\sf \implies$ 8n - 3n = - 3 - 4

$\sf \implies$ 5n = - 7

$\sf \implies$ n = $\tt \frac{-7}{5}$

$\implies \sf n = \sf \frac{-7}{5}$