Log10√35-log10√7+log10√2
this is just log√(35*2/7) = log√10 = 1/2
(35*2/7) = log√10 = 1/2
To simplify the expression log10√35-log10√7+log10√2, we can use the properties of logarithms.
1. Start by simplifying each individual logarithm:
- log10√35 = log10(35^(1/2))
- log10√7 = log10(7^(1/2))
- log10√2 = log10(2^(1/2))
2. Applying the property log10(a^b) = b * log10(a), we can rewrite the expressions with exponents:
- log10(35^(1/2)) = (1/2) * log10(35)
- log10(7^(1/2)) = (1/2) * log10(7)
- log10(2^(1/2)) = (1/2) * log10(2)
3. Substitute the rewritten expressions back into the original expression:
(1/2) * log10(35) - (1/2) * log10(7) + (1/2) * log10(2)
4. Since the exponents are the same for each term, we can factor out the (1/2):
(1/2) * (log10(35) - log10(7) + log10(2))
5. Now, we can combine the logarithms using the properties of logarithms:
log10(35/7) + log10(2)
6. Simplify further by dividing 35 by 7:
log10(5) + log10(2)
7. Apply the property log10(a) + log10(b) = log10(a*b):
log10(5 * 2)
8. Multiply 5 and 2:
log10(10)
9. Finally, since log10(10) = 1, the simplified expression is:
1
To simplify the expression log10√35-log10√7+log10√2, we can use the properties of logarithms.
The first property we can use is the product property which states that log a + log b = log ab. Similarly, log a - log b = log (a/b).
So, we can rewrite the expression as log10(√35) - log10(√7) + log10(√2). Now, let's simplify each term one by one:
1. Simplifying log10(√35):
Using the property log √a = 1/2 * log a, we can rewrite log10(√35) as (1/2) * log10(35).
2. Simplifying log10(√7):
Similarly, log10(√7) can be rewritten as (1/2) * log10(7).
3. Simplifying log10(√2):
Once again, using the property log √a = 1/2 * log a, we can rewrite log10(√2) as (1/2) * log10(2).
Now, let's substitute these simplified terms back into the expression:
(1/2) * log10(35) - (1/2) * log10(7) + (1/2) * log10(2).
Now, we can further simplify this expression by factoring out the common factor (1/2):
(1/2) * (log10(35) - log10(7) + log10(2)).
Finally, we have simplified the expression to (1/2) * (log10(35) - log10(7) + log10(2)).