💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
Get the answer to your homework problem.
Try Numerade free for 30 days
Like
Report
DISCUSS = DISCOVER: The Number of Digits in an IntegerCompare log 1000 to the number of digits in $1000 .$ Do thesame for $10,000$ . How many digits does any number between 1000 and $10,000$ have? Between what two valuesmust the common logarithm of such a number lie? Use yourobservations to explain why the number of digits in any observations to explain why the number of digits in anypositive integer $x$ is $\|\log x\|+1 .$ (The symbol $\|n\|$ is thegreatest integer function defined in Section $2.2 .$ How manydigits does the number $2^{100}$ have?
31
Algebra
Chapter 4
Exponential and Logarithmic Functions
Section 3
Logarithmic Functions
Campbell University
McMaster University
University of Michigan - Ann Arbor
Idaho State University
Lectures
01:32
In mathematics, the absolu…
01:11
01:59
DISCUSS in DISCOVER: The N…
02:45
Compare log 1000 to the nu…
06:10
Deal with iterations of th…
03:25
Consider the function $y=\…
05:14
Prove that if $n$ and $b$ …
00:23
Use your calculator to eva…
01:41
Evaluate each logarithm. <…
01:26
Evaluate each logarithm.
00:47
Evaluate each logarithm. S…
10:44
So we want to find out how many digits two to the power of 100 has. And so So we know that our formula to find the number of digits is this This is greatest manager functions. So this greatest energia is is log of X and then we have we have plus one for this long of X plus one. So all we have to do is is plug in X is equal to two to the 100 into this into this equation. And so this gives us this gives us number of digits. So this is now an equation. Number of digits. And so So if we plug in, if we say log based a log of two to the 100 weaken, weaken, change this 100 make it into our co efficient. So this is equal to 100 times log based too 100 times log base to so plugging this in gives us 100 log base to, and this is remember, inside our greatest energy or function, this is our greatest energy function plus one. And so what this means is that we're going to round down to the nearest whole number regardless of if we have, you know, any decimal places. So 100 times log based to is is equal to is equal to 30 point 30.1. And so, if we round this down, we get this is equal to 30 because we want the integer and then 30 plus one. That means that means this has 31 digits, 31 digits. And so this is this is our solution.
View More Answers From This Book
Find Another Textbook
In mathematics, the absolute value or modulus |x| of a real number x is its …
DISCUSS in DISCOVER: The Number of Digits in an Integer Compare log 1000 to …
Compare log 1000 to the number of digits in $1000 .$ Do the same for $10,000…
Deal with iterations of the logarithm function. Let log $n$ denote the logar…
Consider the function $y=\log \left(10^{n} \cdot x\right)$ where $n$ is an i…
Prove that if $n$ and $b$ are positive integers with $b \geq 2$ the base $b$…
Use your calculator to evaluate each logarithm to four decimal places. Then …
Evaluate each logarithm. $$\log 10,000$$
Evaluate each logarithm.$$\log 10,000$$
Evaluate each logarithm. See Examples 2 and 3.$$\log (10,000)$$
03:44
Electric Circuit After the switch is closed in the circuitshown, the cur…
00:55
$13-28=$ Simplifying Trigonometric Expressions Simplify the trigonometric ex…
01:16
$59-62=$ Composition of Three Functions Find $f \circ g \circ h$$$f(x)=x…
01:13
Sledding The time in seconds that it takes for a sled to slide down a hillsi…
00:59
Logarithmic Equations Solve the logarithmic equation for $x .$$$\log (x-…
01:08
$63-68=$ Expressing a Function as a Composition Express the function in the …
02:46
Circumference of the Earth The Greek mathematician Eratosthenes (ca. 276-195…
02:38
$75-76=$ Revenue, cost, and Profit $A$ print shop makes bumper stickers for …
01:55
$19-34=$ Graphs of Trigonometric Functions with DifferentPeriods Find th…
10:18
Turning a Corner A steel pipe is being carried down a hallway that is 9 ft w…
Create an account to get free access
Join Numerade as a
Already have an account? Log in
