Transcript Example 2 - Mr.Zuccheroso

Properties of Logarithms
Simplify into a single logarithmic expression:
a) log9x4 + 2log3x – 2log2y
log9x4 + log(3x)2 – log(2y)2
log9x4 + log9x2 – log4y2
log 9x4∙9x2
4y2
log 81x6
4y2
Simplify into a single logarithmic expression:
b) 4ln2x + ln(6/x) – 2ln2x
ln(2x)4 + ln(6/x) – ln(2x)2
ln16x4 + ln(6/x) – ln4x2
ln 16x4∙6
x∙4x2
ln 96x4
4x3
ln(24x)
Expand the following logarithmic expressions:
a)
= log33x2 – (log39y)
= log33 + log3x2 – (log39 + log3y)
= 1+ 2log3x – (2 + log3y)
= 2log3x – log3y - 1
b)
= log(y-3)2 – (logy3 + log(x-1))
= 2log(y-3) – 3logy - log(x-1)
Let’s do some more challenging questions…
Example 1:
Given that log34 = x, evaluate log316
Example 2:
If logma = 3 and logmb = 4, evaluate
Example 3:
If
, determine an expression for
logx
Example 4:
2
If logx = 3, evaluate log10x
Example 5:
If log2A = B, then log4A =?
Example 6:
If logab = 0.92, then the value of
is:
Example 7:
If log3x = 20, then the value of
is:
Example 8:
If logx = 3.2 and logy = -0.9, then
Example 9:
logm9 = 2 and log8n = 2, then log2(mn) =
Example 10:
If x = y2z, then find an expression for
logz
Example 11:
If logbA = M, then
Example 12:
If 10a = 4, then 101+2a = ?