solve question number 71
Answers
Answer:
P = 30
Step-by-step explanation:
(71).
a = 1 + log 2 - log 5
b = 2 log 3
c = log P - log 5.
Given:
⇒ a + b = 2c
⇒ (1 + log 2 - log 5) + (2 log 3) = 2(log P - log 5)
⇒ 1 + log 2 - log 5 + 2 log 3 = 2 log P - 2 log 5
⇒ 1 + log 2 + log 5 + 2 log 3 = 2 log P
∴ a log b = log bᵃ
⇒ 1 + log 2 + log 5 + log 3² = 2 log P
∴ 1 = log 10.
⇒ log 10 + log 2 + log 5 + log 9 = 2 log P
∴ log a + log b = log ab
⇒ log(10 * 2) + log(5 * 9) = 2 log P
⇒ log(10 * 2 * 5 * 9) = 2 log P
⇒ log(10 * 10 * 9) = 2 log P
⇒ log(900) = log P²
⇒ 900 = P²
⇒ (30)² = P²
⇒ P = 30.
Therefore, the value of P = 30.
Hope it helps!
If a=1+log2-log 5, & b=2log3 & also log a -log 5
With the help of given equatio a+b= 2c WE can easily find the value of a
1+log2-log5+2log3 = 2log a- log 5
By log base a x power m= m log base a x
So. Log 2 -log 5 +log3^2=2(loga-log5)
By loga-logb= loga/b
So log 2/5+ log9 =log(a/5)^2
= by loga+logb= loga×b
So log 2/5×9=loga^2/5^2
log18/5=loga^2/25
Now cancel log from both side
18/5=a^2/25
18×25/5=a^2
90=a^2
Under root of 90=a
a=30