@2025 everexams.com
📘 Mathematics Test Paper – Class 9th (SNC)

Unit 2: Logarithms
Time: ______
Total Marks: ______
Obtained Marks: ______

Q1. Choose the correct option. (10×1=10)

1. The difference between the standard and current position of decimal:
   (A) Scientific notation
   (B) Ordinary notation
   (C) Coefficient
   (D) Exponent
2. In $5.5\times {10}^{-4}$5.5×10−4, 5.5 and ${10}^{-4}$10−4 are respectively:
   (A) Decimal and power
   (B) Coefficient and exponent
   (C) Decimal and exponent
   (D) Exponent and power
3. ${\log }_{23}1=0$log23​1=0 in exponential form will be:
   (A) ${23}^0=1$230=1
   (B) $23=0$23=0
   (C) $1^0=23$10=23
   (D) $0=23$0=23
4. If $p=q^r$p=qr, then using logarithm, value of $r$r will be:
   (A) ${\log }_{p}q$logp​q
   (B) ${\log }_{q}p$logq​p
   (C) ${\log }_q^p$logqp​
   (D) $p\log q$plogq
5. Express in symbolic form: the logarithm of $x$x to the base $b$b is:
   (A) ${\log }_{x}b=y$logx​b=y
   (B) ${\log }_{b}x=y$logb​x=y
   (C) ${\log }_b=xy$logb​=xy
   (D) None of these
6. For what value of $x$x, ${\log }_2(1024)=x$log2​(1024)=x?
   (A) 8
   (B) 10
   (C) 12
   (D) 14
7. In $\log 3.45$log3.45, the integral part is:
   (A) $\log$log
   (B) 3
   (C) 0.45
   (D) 3.45
8. If $\log 3.177=0.5019$log3.177=0.5019, then $\log 3177$log3177 is:
   (A) 0.5019
   (B) 1.5019
   (C) 2.5019
   (D) 3.5019
9. If $\log x=0.0065$logx=0.0065, the value of $x$x will be:
   (A) 0.015
   (B) 1.015
   (C) $-2.187$−2.187
   (D) 2.187
10. The inverse operation of logarithm is:
    (A) Common logarithm
    (B) Natural logarithm
    (C) Antilogarithm
    (D) None of these

Q2. Write short answers to the following questions. (15×2=30)

[1] Express the following number in scientific notation: $73\times {10}^3$73×103
[2] Express the following number in ordinary notation: $5.5\times {10}^{-4}$5.5×10−4
[3] Express the following number in ordinary notation: $4\times {10}^{-5}$4×10−5
[4] The diameter of Earth is about $1.2756\times {10}^4$1.2756×104 km. Express this number in standard form.
[5] Express the following in exponential form: ${\log }_{4}16=4$log4​16=4
[6] Express the following in exponential form: $5={\log }_{10}100000$5=log10​100000
[7] Express the following number in ordinary notation: $8.794\times {10}^{-4}$8.794×10−4
[8] Express the following in logarithmic form: ${12}^2=144$122=144
[9] Express the following in exponential form: ${\log }_{9}729=3$log9​729=3
[10] Write the general form of a logarithm.
[11] Define Common Logarithm.
[12] Define Mantissa of a logarithm with an example.
[13] Differentiate between Common and Natural Logarithms.
[14] Express the following in exponential form:
 (i) $5={\log }_{10}100000$5=log10​100000
 (ii) ${\log }_2\frac{1}{8}=-3$log2​81​=−3
[15] Calculate the value of $x$x, if ${\log }_{8}8=1$log8​8=1

Q3. Write detailed answers to the following questions. (Answer any 2) (2×5=10)

1. Expand the following using laws of logarithms:$$\log (xy{z}^4)$$log(xyz4)
2. Expand the following using laws of logarithms:$${\log }_3\sqrt[6]{m^5{n}^3}$$log3​6m5n3​
3. Expand the following using laws of logarithms:$$\log \sqrt{8x^3}$$log8x3​

End of Paper
© 2025 everexams.com | All rights reserved.