Final answer:
The question involves using logarithmic identities to express a given quantity in terms of 'a' and 'b', where 'a' and 'b' represent the logarithms of 7 and 3, respectively. By applying properties of logarithms such as those for multiplication, division, and exponentiation, one can rewrite complex logarithmic expressions in terms of 'a' and 'b'.
Step-by-step explanation:
The student has been asked to express a given logarithmic quantity in terms of the variables a and b, where a=log(7) and b= log(3). To do this, we use logarithmic identities. There are several important properties of logarithms to remember:
- The logarithm of a product is the sum of the logarithms of the factors: log(c × d) = log(c) + log(d).
- The logarithm of a quotient is the difference between the logarithms of the numerator and the denominator: log(c/d) = log(c) - log(d).
- The logarithm of a number raised to an exponent is the exponent multiplied by the logarithm of the number: log(c^n) = n × log(c).
Using these properties, the student can rewrite complex logarithmic expressions in terms of a and b. For example, if the student needs to express log(21) in terms of a and b, they would use the product rule because 21 can be written as 7 × 3, which in turn is log(7) + log(3) or a + b.