Question

For each of the following logarithmic expressions, give the two integers that its value falls between. The first one is done for you. Hint: Remember that logarithms represent exponents.

The value of log3(150) is greater than -4 and less than -3 because 3^-4=181 and 3^-3=127.
a. The value of log5(2350) is greater than _____but less than _______.
b. The value of log10(113,700) is greater than_____ but less than _______.
c. The value of log2(1144) is greater than___________ but less than________.

Answer 1

Explanation:

a )

5⁵ = 3125 and 5⁴ = 625

log5(3125) = 5 and log5(625) = 4

so log5(2350) will be greater than 4 but less than 5 .

b )

10⁶ = 1000000 and 10⁵ = 100000

log10( 1000000) = 6 and log10( 100000) = 5

log(113700) will be greater than 5 but less than 6

c )

2¹¹ = 2048 and 2¹⁰ = 1024

log2( 2048) = 11 and log2(1024) = 10

log2(1144) is more than 10 but less than 11 .