Question

a) Convert log x=t into an exponential equation. b) Convert 3-2 = into a logarithmic equation. 9 Use the change of base formula to find log; 5 to four decimal places.

Answer 1

Solution:

The values provided in the questions are

a) log_c x = t into exponential equation

we know that formula

y = log_b c

==>  b^y = c -------------------------------->1

substitute equation 1 rule into given equation

x = c^t

Result:

x = c^t

b) 3^-2 = 1/9 into an logarthmic equation

3^-2 = 1/9 -------------------------->2

we kow that formula

b^-y = 1/c

==> log_b(1/c) = - y ------------------>3

Substitute equation 3 rule into equation 2

-2 = log₃(1/9)

Result:

log₃(1/9) = -2

c) Use the change of base formula to find log₃(5) to four decimal places

= log₃(5) --------------------------------->4

we know that formula

log_a(x)=log_c(x) / log_c(a)​ -------------------->5

substitute equation 5 rule into equation 4

  log₃(5) = log₁₀(5) / log₁₀(3)

log₃(5) = 0.6989 / 0.4771

log₃(5) = 1.46497