Solutions to exponential inequality and logarithmic inequality

Solutions to exponential inequality and logarithmic inequality

If the power of B of a (a > 0, and a ≠ 1) is equal to N, that is ab = n, then the number B is called logarithm with a as the base n, denoted as Logan = B, where a is called the base of logarithm, and N is called the true number. It is known from the definition that: ① negative number and zero have no logarithm; ② a > 0 and a ≠ 1, n > 0; ③ loga1 = 0, logaa = 1, Logan = n, logab = B. in particular, logarithm with 10 as the common logarithm, denoted as log10n, In short, it is LGN ）The logarithm with base is called natural logarithm, which is called LOGEN, and is abbreviated as lnn. 2 the name of reciprocal formula of logarithm formula and exponential formula ABN exponential formula AB = n (base) (index) (power value) Logan = B (base) (logarithm) (true number) 3 the operational properties of logarithm if a > 0, a ≠ 1, M > 0, n > 0, Then (1) loga (MN) = logam + Logan. (2) logamn = logam Logan. (3) logamn = nlogam (n ∈ R), N> 0? ② logaan =? (n ∈ R) ③ comparison between logarithm formula and exponential formula. (students fill in the table) formula AB = nlogan = B name the base of a-power b-n-a-logarithm b-n-operation property am · an = am + n am △ an = (AM) n = (a > 0 and a ≠ 1, n ∈ R) logamn = logam + Logan logamn = logamn = (n ∈ R) (a > 0, a ≠ 1, M > 0, n > 0), Why should a > 0 and a ≠ 1 be specified? The reasons are as follows: ① if a < 0, then some values of n do not exist, such as log-28; ② if a = 0, then n ≠ 0, B does not exist; when n = 0, B is not unique and can be any positive number; ③ if a = 1, then n ≠ 1, B does not exist; when n = 1, B is not unique and can be any positive number