Question

Find the value of n in the exponent: 2^11 /2^6=2^3*2^2n-1

Answer 1

Step-by-step explanation:

How to solve for exponents

xn=y. Take the log of both sides:

logxn=logy. By identity we get:

n⋅logx=logy. Dividing both sides by log x: n=logylogx. Find the exponent of a number. ...

3n=81. Take the log of both sides:

log3n=log81. By identity we get:

n⋅log3=log81. Dividing both sides by log 3: n=log81log3.

Answer 2

Answer:

$\frac{ {2}^{11} }{ {2}^{6} } = {2}^{3} \times {2}^{2n - 1} \\ \\ {2}^{11 - 6} = {2}^{3 + 2n - 1} \\ \\ {2}^{5} = {2}^{2n + 2} \\ \\ \color{blue}{ \underline{on \: comparing} : } \\ 5 = 2n + 2 \\ 2n = 3 \\ \boxed{n = \frac{3}{2} } \\ \\ \red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$