Write down the values of (1) loga(a) and (2) loga(a^3) [(1) log base a, of a (2) log base a of (a^3)]

Let's first go to the whiteboard where I will explain what a logarithm is. The equation, loga(b) = x, could be re-written into the form, a^x = b. This is true for all logarithmic equations. There is a rule for logarithmic equations, if the element in the place of "b" (the letter does the have to be "b", could be any letter or number providing that the number is greater than 0) is raised to a power, the power can then become a coefficent of the equation and "b" would then be raised to the power 1. This will be made clear with the following example: loga(b^2) = x This equation is equivilant to: 2loga(b) = x So now let's use what we have learnt to answer the two parts of the question. (1) loga(a). This is the same as writing a^x = a. The only possible solution to this equation is for x to be equal to 1, as any number raised to the power 1 will just give the same number, e.g. 2^1 = 1 31^1 = 31 999^1 = 999 (2) loga(a^3) This is the same as, 3loga(a) We already have the value of loga(a) from (1), it is 1, so 3loga(a) must be 31, which is equal to 1. Are there any questions, or is there anything that you would like me to go over again?