Logarithms Algebra II

From Log to Exponential

100

log(x)=y

10^y=x

200

The log, base 4, of 64 is 3. 

4³=64

300

log₂(42)=x

2^x=42

400

the log of 80 equals x

10^x=80

500

log_(1/2)(y)=12

(1/2)¹²=y

Properties of Logs

100

log(2)+log(5) = log(?)

log(10)

200

log(2)-log(5)=log(?)

log(2/5)=log(0.4)

300

log(30) = log(?)-log(?)

The ? are any two numbers such that the first number divided by the second number equals 30.

400

log(?)-log(7)=log(126)

? = 882 because 882/7=126

500

If xlog(3) equals log(81), what is x? 

xlog(3) = log(3^x) 

3^x = 81
x=4

Properties of Logs

100

How can you rewrite xlog(30)? 

log(30^x)

200

log(90)=log(?)+log(?)

The ? are any two numbers that multiply to 90

300

log(13)+log(?)=log(104)

? = 8 because 13*8=104

400

What is the quotient property of logs? 

log(b)-log(a)=log(b/a)

500

if log(16384)=xlog(4), what is the value of x?

log(16384)=log(4^x)

4^x=16384
x=7

From Exponential to Log

100

2^y=x

log₂(x)=y

200

3^x=y

log₃(y)=x

300

t²=9

log_t(9)=2

400

b^y=x

log_b(x)=y

500

d^h=u

log_d(u)=h

Solve for the Variable

100

1.05^x=5

x~33

200

2.2^x=1

x=0

300

3.21^x=29

x~2.89

400

(1/2)^x=4

x=-2

500

2(3^x)=1062882

x=12