Exponentials and Logarithms

Theory

100

True or false? The domain on a logarithmic funtion is always all real numbers

False

200

The base of the natual logarithm is...

euler

300

The function y=log(x-7)+2 shows a translation of...

7 units to the right and 2 units up

400

A logarithm with a base bigger than one will show a behavior of....

Growth

500

the propery that allows us to bring the exponent in front as a multiplier

 power

Exact answers

100

A logarithm with an argument of 1 equals....

zero

200

log₃(x+2)=-1

x=-5/3

300

4^x-1=16^x+3

x=-7

400

log₅(2x+3)=log₅(x-6)

x=-9

500

log₂(x+5)=2-log₂(x+8)

x=-4

Expanding

100

property that says the logarithm of a product is equal to the sum of the logarithm of the factors

product property

200

log(y⁵z)

5logy+logz

300

log(z³/yx)

3logz-logy-logx

400

log√(xy⁷/z³)

1/2logx+7/2logy-3/2logz

500

log√((x+6)³/x⁵)

3/2log(x+6)-5/2logx)

Condensing

100

property that says the logarithm of a quotient is equal to the difference of the logarithm of the factors.

quotient property

200

log(x)+4log(y)

log(xy⁴)

300

4logz-2logx-logy

log (z⁴/x²y)

400

2(logy-5logw)+3logz

log(y²z³/w¹⁰)

500

2(1/2logw-3logy)+1/3logz

log((w³√ z)/y⁶)