C2 logs question

I lost three marks for this question, but I don't know whether it was simply for my working out (which was a bit weird after I changed the base) or whether I got the answer totally wrong as well.

Could someone show me the working out and correct answers for this?

Qu: Calculate the values of Z.

log3Z = 4logz3

(to the base 3 and then to the base Z)

Thank you in advance.

Reply 1

insparato

I havent done logs in a while so this was quite refreshing. Okay

Log3z = 4logz3 ----- This tells me change base i prefer to change to three

log3z = 4log3 3/log 3z ---- log 3 3 = 1 changing base is log a b = logca/logcb

therefore

log 3 z = 4 x 1/log3z

Now multiply both sides by log3z

(Log3z)^2 = 4

Square root both sides

Log3z = 2 or -2 - square root of 4 is 2 and -2

Now log ab = x when a^x = b so

z = 3^2 = 9
z = 3^-2 = 1/9

I know these are right because they are the answers in the back of the heinemanns C2 book.

Really got me into doing some earlier C2 if you need anymore help on 3G mixed exercise just tell me ive done all the questions. [email protected]

Reply 2

TheThief

Thanks for that Aaron, after this test I started working through 3G as a bit of revision and I didn't realise that it was the same question, but I was confused about getting the 1/9. :biggrin: