Exponential and Logarithmic Functions

Expanding Logs

100

log_8 4xy

log_8 4+log_8 x +log_8 y

200

ln(y^3/z^4)

3lny-4lnz

300

log(sqrt(xy))

1/2logx+1/2logy

400

log_n sqrt(b^4/(a^7c^3))

2log_n b - 7/2log_na - 3/2log_n c

Condensing Logs

100

log_x 9 + log_x 5

log_x 45

200

4logh - 3log5

log (h^4/125)

300

5ln2 - 3ln4

ln (1/2)

400

log_6x/2+5log_6 y + 3log_6 z/2

log_6 sqrtxy^5sqrt(z^3)

Logarithmic Equations

100

log(2x+5)=log9

x=2

200

log_4(3x-2)=2

x=6

300

ln(2x+3)=5

(e^5-3)/2

400

log(2x-1)+logx=1

x=5/2, x=-2 (e.s.)

Exponential Equations

100

2^x=16

x=4

200

-27^x=-9

x=2/3

300

5^(2x)+3=10

x=(log_5 7)/2

400

-8e^(5y-7)-13=-45

(ln4+7)/5

Log/Exponential Forms

100

Rewrite the following in exponential form.

log_4 16 = 2

4^2=16

200

Rewrite the following in logarithmic form.

6^(x+4)=14

log_6 14 = x+4

300

Rewrite the following in exponential form.

1/3logy=6

10^18=y

10^6=y^(1/3)

400

Write the following in logarithmic form.

4e^(2x+3)=15

ln(15/4)=2x+3