Logarithmic equations

converting between exponential and logarithmic forms

100

log₃(6)=2 transitioned into 3²=6, what form is this changing to?

What is Exponential?

200

6⁴=1296, if 6 is represented by "X" what place in the formula would it be transitioned into in logarithmic?

ex. x^z=y -> log_{(spot 1)}^{(spot 2)}=(spot 3)

What is Spot 1?

300

of (spot 4)_{(spot 3)}^{(spot 2)}=(spot 1), What spot would "log" be placed?

What is Spot 4?

400

log₂512=9 in exponential form

What is 2⁹=512?

500

convert log₅(2x-1)=3 into exponential form

5³=2x-1

evaluating logarithms(with and without a calculator)

100

log(100)

What is 2?

200

log₂(8)

What is 3?

300

log₅(125)

What is 3?

400

log₃√3

What is 1/2?

500

In order to get 1/16th, what exponent would you raise 2 to?

What is -4?

Condense logarithms

100

log(x)+log(5)

What is log(5x)?

200

log(x)-log(2)

What is log(x/2)?

300

3log(x)+log(y)

What is log(x³y)?

400

log(a)+log(b)-2log(c)

What is log(ab/c²)?

500

2log(x-1)+log(x+3)-log(2) Condensed is:

Log((x-1)²(x+3))/2

logarithmic equations

100

log(x)=3

What is x=1000?

200

log₂(x-1)=3

What is x=9?

300

The first step in solving log(x)=3?

What is rewrite as 10³=x?

400

Why does X have to be >0 in logarithmic equations>

Because logarithmic equations can only be solved with positive numbers.

500

What someone needs to do to check their answers.

What is plugging in their variables?

exponential equations that require logs

100

2^x=8

What is X=3?

200

10^x=50

What is x=log(50)

300

How you approach a problem like 3^x=7

What is taking the logs on both sides?

400

5^x=20 rewritten using logarithms

What is x=log(20)/log(5)?

500

Taking log of both sides log(4^x)=log(7), x=log(7)/log(4)

What is the first and last steps of solving 4^x=7?