if a=log 7, b=log 2, express log 35 in terms of a and b?
What does * mean
i am not satisfied
To express log 35 in terms of a and b, we can use logarithmic properties and the change of base formula.
We know that log 35 is not directly given in the problem, but we can express 35 as a product of prime factors: 35 = 5 * 7.
Now, we can write log 35 as the sum of logs of its prime factors:
log 35 = log (5 * 7)
Using the logarithmic property, this can be written as:
log 35 = log 5 + log 7
To express this in terms of a and b, we need to use the given information:
a = log 7 (given)
b = log 2 (given)
Now, we can use the change of base formula, which states that for any positive numbers x and y, and any positive base z, log base z of x is equal to log base y of x divided by log base y of z:
log x (y) = log z (y) / log z (x)
Applying the change of base formula, we get:
log 35 = log 5 + log 7
= log (5 * 7)
= log (7^1) + log (7^1)
= 1 * log 7 + 1 * log 7
Using the given information, we substitute the value of a for log 7:
log 35 = 1 * a + 1 * a
= 2a
Therefore, log 35 can be expressed as 2a in terms of a and b.
35 = 7*10/2
log 35 = log (7*10/2)
= log 7 + log 10 - log 2
= a + 1 + b