To determine

To find:

(a) Exact Value of log51125

(b) Exact Value of ln1e2

Answer

(a) -3

(b) -2

Explanation

Calculation:

(a)

Given data: log51125

Formula used: logbx=y  ⇔  x=by.

log51125=−3 because 5−3=1125

Thus, exact value of log51125 is −3_

(b)

Given data: ln1e2

Formula used: lnx=logex=y  ⇔  x=ey.

ln1e2=loge1e2=y

1e2=ey⇔e−2=ey

y=−2

Thus, Exact Value of ln1e2 is −2_

Final statement:

(a) -3

(b) -2