log(1+1/root 2) to the base root 2 + log(1-1/root 2) to the base root 2 =
Answers
Answer:
What is the value of log of (1/256) to the base 2√2?
We are required to find the value of log of (1/256) to the base 2√2.
I shall write the base of the log within parenthesis, first the base followed by the number whose log we wish to determine.
log [2√2, (1/256)]
= log [√8, (1/2)⁸]
= log [√8, (2)^-8]
= log [√8, (√2)^-16]
= log [√8, {(√2.√2.√2)⅓}^-16]
= log [√8, (√8)^-¹⁶/³]
= (- 16/3) log [√8, √8]
= (- 16/3) . 1
= - 16/3.
Step-by-step explanation:
log
2
2
x=
3
a
Step-by-step explanation:
Given :
log_{\sqrt{2}} \ x=alog
2
x=a
Then,
find the value of :
log_{2\sqrt{2}} \ xlog
2
2
x
Solution :
We know that,
log_{a^n} \ b=\frac{1}{n}log_{a} \ blog
a
n
b=
n
1
log
a
b
Also,.
We know that,
2 × √2 = (√2)² × √2 = (√2)³
So,
⇒ log_{2\sqrt{2}} \ x=log_{(\sqrt{2})^3} \ x=\frac{1}{3}log_{\sqrt{2}} \ b=\frac{1}{3}(a) = \frac{a}{3}log
2
2
x=log
(
2
)
3
x=
3
1
log
2
b=
3
1
(a)=
3
a
∴ log_{2\sqrt{2}} \ x = \frac{a}{3}log
2
2
x=
3
a