http://www.ck12.org Chapter 3. Logs and Exponents
False. It is true that the log of a product is the sum of logs. It is not true that the product of logs is the log of a sum.
Practice
Decide whether each of the following statements are true or false. Explain.
1.loglogxy=log
(x
y)
2.(logx)n=nlogx
- logx+logy=logxy
Rewrite each of the following expressions under a single log and simplify. - log 4x+log( 2 x+ 4 )
- 5 logx+logx
- 4 log 2 x+^12 log 29 −log 2 y
- 6 log 3 z^2 +^14 log 3 y^8 −2 log 3 z^4 y
Expand the expression as much as possible. - log 4
( 2 x 3
5)
- ln
( 4 xy 2
15)
- log
(x (^2) (yz) 3
3
)
Translate from exponential form to logarithmic form.
2x+^1 + 4 = 14
Translate from logarithmic form to exponential form.
log 2 (x− 1 ) = 12
Prove the following properties of logarithms.
logbnx=^1 nlogbx
logbnxn=logbx
log (^1) b^1 x=logbx