How Do I answer these questions?

Question

(a)log 2 8 = 3 can be written in the form 2^A = B where

A= B=

(b) log 5 25 = 2 can be written in the form 5^C = D where

C= D=

(c)log 81 ( 3 ) = 1/4 is equivalent in exponential form to

(D)Evaluate log 1/10( 100 ) without using a calculator.

Answer 1

a) log₂(8) = 3 The rule is take the base of the log (2), raise it to the power on the right hand side of the equation (3), and that equals the number you're taking the log of (8), so 2³ = 8. You try it on b) and c).

d) log_1/10(100) = ? The trick here is to write 100 as a power of 1/10. The answer is 100 = (1/10)^-2. So you have log_1/10((1/10)^-2) = ? . The rule to use is log_a(a^x) = x. In your case, a = 1/10 and x = -2.

Answer 2

(a) log₂8 = 3 can be written as →

2³ = 8

A = 3, B = 8

(b) log₅25 =2 can be written as →

5² = 25

C = 2, D = 5

(c) log₈₁3 = 1/4

81^1/4 = 3

(d) log_1/10100 = x

(1/10)^x = 100

(10^-1)^x =10²

-x = 2

x = -2