math 114 test 3 week 8

whenever ____ is the input of log what does it =? ex log10 (1)

0

b^0 =1

1 ex) b^0=1 logb^(x)=y<----> b^y=x =logb^1 +0 y=0, x=1, b=b

recipe for log equations

1) Restrictions 2) Logs on 1 side/ everything else on the other 3) Condense the logs 4) translate (get rid of logs) 5) solve 6) check

expand log4(16 square root of xy)

1) use product prop = log4 (16)+log4( square root of xy) =log4(4)^2 + log4 (xy)^1/2 = 2 +1/2log4(xy) =2+1/2[log4(x) +log4 (y)] = 2+1/2log4(x)+1/2log4(y) ----> final answer

inverse of the common log : log10(x)

1og(x)

convert lnx^2

2lnx

logb (x) = y

<----> b^y=x

how to convert lnx(2)

= ln(x*x)= ln(x) + ln(x) = 1 ln+1 ln =2ln(x)---> FINAL ANSWER

log (1/x)

=log10 (1) -log10 (x) = 0 - log(x) = -log(0)

what is the base of logE(x) or base of the natural log

E

how do you convert this? Log7(10x)

Log7(10)+log7(x)

x = about 0.549 is what type of answer

approximate answer of ask to round/ word problems

b^1

b logb(b)=1

inverse of logb(x)

b(x)

expo form

b^y=x b=base y=expo

e^3=log(y)

ex) 3=logE(y) =3logE(y) =3ln(y)

x=e^-3/5 is what type of answer

exact/ answer to solve

something always has to be _____ the log

inside

inverse of the natural log: logE (x)

ln

convert log2 (10/37)

log2 (10) -log2 (37)

How do you convert? Log6(54)

log6 (9*6) = log6 (9*6) = log6 (9) +log6 (6) = log6 (9)+ 1 ----> FINAL ANSWER

log8 (3x^2)

log8(3x^2)= log8(3) +log8(x^2) =log8(3)+2log8(x) -----> final answer

Quotient property convert

logb (M/N) = logb (M)- logb (N)

Product Property

logb (m*n) = logb (m) + logb (n)

power property

logb(M)^p=p *logb(M)

Change-of-Base Formula for Logarithms

logb(x)= logx/logb ex) log5(87) = log87/log5 = about 2.775 bc round 3 decimal places (final answer)

log(1/x)

logx^-1 =(-1)logx =-logx ----> Final answer because x^-1 = 1/x^1 = 1/x

to condense logs what must you do?

reduce to one log w a coeff of one ex) log8(5)+log8(x) = log8(5x) ex)log6(12)-log6(2)= log6(12/2) = log6(6) = 1 ----> final answer

convert log3( square root of x)

square root of x = x^1/2 =1/2log3 (x)

b^x=b^x

x---->x

log form

y=logbx y=expo b=base