So we now started doing logarithms in class and it's surely abstract at first but pretty fun once you get the jist of it.

However I have a question that is supposedly to be on the "higher level" in the book that I don't understand and this is:

lx x = 2lg 8

So x = 64 according to the answer sheet.

But lg 8 is 0.90

And since we have 2lg8 I guess it's 0.90x2 = 1.80

x isn't 1.80 so where did I go wrong? I understand all other aspects of logarithms at the earlier stage though but this is where I stumbled upon problems

__

For example: 31 x 2^5x = 101 is no problems for me:
2^5x=101/31

2^5x=3,26

Lg2^5x = Lg3,26

x(Lg2^5)/Lg2^5 = Lg3,26/Lg2^5

x = 0,34

But what about the problem above?
Thanks in advance!

I assume it’s supposed to be either

Log(x) = 2 Log(8)

Or

ln(x) = 2 ln(8)

In either case, logarithms have properties which you will need to know to work with them. The ones applicable here are:

Log(a^b) = b Log(a)

and for whichever Log you use (log base 10 or natural log, base e) the base raised to the log of something is that something. In the case of Log (base 10):

10^(Log(a)) = a

If you were working with natural log: e^ln(a) = a



So for your problem, you ignored the log that is being applied to the x. X doesn’t equal 2 Log(8). Log(x) = 2 Log(8).

So, you should apply the first property I mentioned. Then solve for x by raising both sides of the equation to the base of the log.

Log(x) = 2 Log(8)
Log(x) = Log (8^2)
Log(x) = Log(64)
10^Log(x) = 10^Log(64)
x = 64

This post was edited by timmayX on Mar 13 2018 09:08pm