4. What is the greatest number that can be written with 3 digits?
Answer: 999
If you are asking the greatest number without repeating the digit, the answer is 987.
5. Which is bigger, 106 or 11%?
This is kinda confusing. Well, this depends on what you mean by 11%. Is it 11% of 100 or a much bigger number? Kindly please rephrase the question.
In case you are not familiar with solving using logarithm, you can try trial and error as long as you are familiar with multiplication table and the table of squares, cubes, and quadroots.
Answers & Comments
Answer:
Let nn be the "number" we are looking for.
1. The number that is equal to 100 when it is squared.
\begin{gathered}[Sol]\\n^2=100\\log_b(100)=2\\b=\sqrt{100}\\b=10\\\therefore\ (\bold{10})^2=100\\\\\text{Answer:}\ \bold{10}\end{gathered}
[Sol]
n
2
=100
log
b
(100)=2
b=
100
b=10
∴ (10)
2
=100
Answer: 10
2. The number that equals 27 when it is cubed.
\begin{gathered}[Sol]\\n^3=27\\log_n(27)=3\\n=^3\sqrt{27}\\n=3\\\therefore(\bold{3})^3=27\\\\\text{Answer:}\ \bold{3}\end{gathered}
[Sol]
n
3
=27
log
n
(27)=3
n=
3
27
n=3
∴(3)
3
=27
Answer: 3
3. What is the whole number when raised to the fourth power is equal to 1296?
\begin{gathered}[Sol]\\n^4=1296\\log_n(1296)=4\\n=^4\sqrt{1296}\\n=6\\\therefore(\bold{6})^4=1296\\\\\text{Answer:}\ \bold{6}\end{gathered}
[Sol]
n
4
=1296
log
n
(1296)=4
n=
4
1296
n=6
∴(6)
4
=1296
Answer: 6
4. What is the greatest number that can be written with 3 digits?
Answer: 999
If you are asking the greatest number without repeating the digit, the answer is 987.
5. Which is bigger, 106 or 11%?
This is kinda confusing. Well, this depends on what you mean by 11%. Is it 11% of 100 or a much bigger number? Kindly please rephrase the question.
In case you are not familiar with solving using logarithm, you can try trial and error as long as you are familiar with multiplication table and the table of squares, cubes, and quadroots.