Help me solve these question
IF LOGA IS 7 AND B=LOG2 EXPRESS LOG35 IN TEARM OF A AND B.
A = log(7) , B = log(2) , log(10) = 1
log(35) = A + 1 - B
log 35
= log (7*10/2)
= log7 + log10 - log2
= log7 + 1 + B
did you mean to say: log7 = A ???
then carry on from my last line
To express log35 in terms of a and b, we need to use logarithmic properties and rules.
First, let's look at the given information:
logᴀ = 7
b = log₂
To express log35, we can use the change of base formula. The change of base formula allows us to change the base of the logarithm from one number to another. In this case, we want to change the base from 10 (which is the default base of logarithms in most calculators) to a combination of a and b.
The change of base formula is: logᵦ(x) = logₐ(x) / logₐ(ᵦ)
Applying the change of base formula, we get:
log35 = logₐ(35) / logₐ(ᵦ)
Now, we need to find a common base to use in both the numerator and denominator. Since logₐ(7) is given and we want to express log35 in terms of a and b, let's choose a as the common base.
So, log35 = logₐ(35) / logₐ(ᵦ)
To express logₐ(35), we can further apply another logarithmic rule: logₐ(x^y) = y * logₐ(x)
Since 35 = 7 * 5, we can rewrite logₐ(35) as logₐ(7 * 5).
Using the logarithmic property mentioned above, we have:
logₐ(35) = logₐ(7) + logₐ(5)
Replacing logₐ with the given value of 7, we get:
logₐ(35) = 7 + logₐ(5)
Finally, substituting this expression into the equation from earlier, we have:
log35 = (7 + logₐ(5)) / logₐ(ᵦ)
Thus, log35 can be expressed in terms of a and b as:
log35 = (7 + logₐ(5)) / logₐ(ᵦ)