Simplify or Evaluate a Logarithmic Expression

The question asks the student to compute the numerical value of an expression composed of logarithms (and possibly exponentials) using laws of logarithms such as product, quotient, power, and change-of-base rules.

turkey-yks 2019 Q15 View
Ada calculates the value of $\log _ { 2 } n$ on her scientific calculator for every positive integer n where $\mathrm { n } \leq 32$, and observes that each value is either an integer or a decimal number. Ada writes down either the number itself if the value displayed on the screen is an integer, or the integer part of the number if it is a decimal, and then finds the sum of these numbers she wrote down. Accordingly, what is the result of the sum that Ada found?
A) 94
B) 97
C) 100
D) 103
E) 106
turkey-yks 2021 Q13 View
On a calculator, when an operation is performed, the machine displays the result as a whole number if the result is an integer, or displays the integer part along with the first two decimal places after the decimal point if the result is a decimal number.
When Nevzat performs the operation $\ln ( 9{,}6 )$ on this calculator, he sees the value 2.26 on the screen, and when he performs the operation $\ln ( 0{,}3 )$, he sees the value $-1{,}20$ on the screen.
When Nevzat performs the operation $\ln ( 0{,}5 )$ on this calculator, what value does he see on the screen?
A) $-0{,}61$
B) $-0{,}65$
C) $-0{,}69$
D) $-0{,}73$
E) $-0{,}77$