Use the change-of-base formula to evaluate each logarithm correct to six decimal places.(a)log7(35) (b)log18(14)

(a) log7(35)

The change of base formula is logb(a) = logc(a) / logc(b). We can use this formula to change the base to 10 because most calculators use base 10.

So, log7(35) = log10(35) / log10(7)

Using a calculator, we find that log10(35) ≈ 1.544068 and log10(7) ≈ 0.845098

Therefore, log7(35) = 1.544068 / 0.845098 ≈ 1.827369

(b) log18(14)

Similarly, we can use the change of base formula to change the base to 10.

So, log18(14) = log10(14) / log10(18)

Using a calculator, we find that log10(14) ≈ 1.146128 and log10(18) ≈ 1.255273

Therefore, log18(14) = 1.146128 / 1.255273 ≈ 0.913004

So, log7(35) ≈ 1.827369 and log18(14) ≈ 0.913004 to six decimal places.