2²⁰⁰ × 3¹⁰ = ?, if log2= 0.30103, log3= 0.47712
Answers
Step-by-step explanation:
Given:-
log2= 0.30103, log3= 0.47712
To find:-
Find the value of 2²⁰⁰ × 3¹⁰ ?
Solution:-
Given that :-
log2= 0.30103,
log3= 0.47712
Now 2²⁰⁰ × 3¹⁰
Let X=2²⁰⁰×3¹⁰
On taking logarithms both sides
=>log X=log [2²⁰⁰×3¹⁰]
we know that
log (a×b)=log a + log b
=>log X=log 2²⁰⁰ + log 3¹⁰
we know that log a^m=m log a
=>log X= 200 log 2 + 10 log 3
On Substituting the values of log 2 and log 3 then
=>log X= 200(0.30103)+10(0.47712)
=>log X= 60.206+4.7712
=>log X= 64.9772
Characteristic=64
Number of digits =Characteristic+1
Number of digits =64+1=65
It gives that The number of digits in 2²⁰⁰×3¹⁰ =65
we have
log X=64.9772
=>X=anti log of 64.9772
=>X=9.4888×10⁶⁴
X=0.94888×10⁶⁵
Answer:-
The number of digits in 2²⁰⁰×3¹⁰=65
The value of 2²⁰⁰×3¹⁰=0.9488×10⁶⁵
The standard form = 9.488×10⁶⁴
Step-by-step explanation:MUR RESULTS SUA....HEEHE
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