DJ Henson's Unit 6: Analysis of logarithmic functions

Exponential equation related to the log

100

Write an exponential equation that is related with the given logarithmic equation:

log₃₆6=1/2

\|-- 36=6

^

^That is my version of a square root

200

Write an exponential equation that is related with the given logarithmic equation:

log₉243=5/2

9^5/2=243

300

Write an exponential equation that is related with the given logarithmic equation: 

log₄1/16=-2

4^-2=1/16

400

Write an exponential equation that is related with the given logarithmic equation: 

log₅1/125=-3

5^-3=1/125

500

Write an exponential equation that is related with the given logarithmic equation:

log₁₀0.000001=-6

10^-6=0.000001

Developing the natural base

100

USING A CALCULATOR Find the value of loga/logb from the following expression of log_ba:

log₃20

log20/log3=2.727

200

USING A CALCULATOR Find the value of loga/logb from the following expression of log_ba:

log₂1/16

(log1/16)/(log2)=-4

300

USING A CALCULATOR Find the value of loga/logb from the following expression of log_ba:

log₅15

log15/log5=1.683

400

USING A CALCULATOR Find the value of loga/logb from the following expression of log_ba:

ln(x+3)=5

e⁵=x+3

145.413=x

500

USING A CALCULATOR Find the value of loga/logb from the following expression of log_ba:

log₂9=x+2

2^x+2=9

1.170=x

Properties of Logarithms

100

Rewrite each expression as a rational number or a single logarithm of the same base:

log₂6+log₂8/3

log₂(16)

4

200

Rewrite each of the following logarithmic expressions as multiple logarithms in expanded form.

log₃xy²

log₃x+2log₃y

300

Rewrite each of the following logarithmic expressions as multiple logarithms in expanded form.

ln(ab/c²)

lna+lnb-2lnc

400

Using the inverse properties of the exponential and logarithmic expressions, simplify the expressions given.

e^ln(x+2)

x+2

500

Using the inverse properties of the exponential and logarithmic expressions, simplify the expressions given.

5^2+log5x

25x

Solving exponential and logarithmic equations

100

Solve for the following exponential equations. ROUND ANSWER TO THREE DECIMAL POINTS.

3e^2x+1=12

x=.193

200

Solve for the following exponential equations. ROUND ANSWER TO THREE DECIMAL POINTS.

3e^x-1+1=10

x=2.098

300

Solve for the following exponential equations. ROUND ANSWER TO THREE DECIMAL POINTS.

8^x-1=2^3x+4

no solution

400

Solve for the logarithmic equation. ROUND ANSWER TO THREE DECIMAL POINTS IF NECESSARY.

log(x+3)+logx=log10

x=2

500

Solve for the logarithmic equation. ROUND ANSWER TO THREE DECIMAL POINTS IF NECESSARY.

-3+ln(2x-1)=-1

x=4.195