Exponential and Logarithm Properties

Question 1

log_a(xy)

Answer 1

log_ax + log_ay

Question 2

log_a(x)^r

Answer 2

r*log_ax

Question 3

log_a(x/y)

Answer 3

log_ax - log_ay

Question 4

EX.

ln(1/e)

Answer 4

= ln(e^-1)

= -ln(e¹)

= -1

OR

= ln(1) - ln(e)

= 0 - 1

= -1

Question 5

loga(a^x)

log₁₀(10⁴)

Answer 5

x

4

Question 6

log_a1

Answer 6

1

Question 7

log_aa

Answer 7

1

Question 8

y = log_ax

Answer 8

a^y = x

Question 9

Base Change Formula:

log_ax

Answer 9

lnx/lna

Question 10

a^x * a^y

Answer 10

a^x+y

Question 11

(a^x/a^y)

Answer 11

a^x-y

Question 12

(ab)^x

Answer 12

a^xb^x