Topics

# Find the value of $$\Large \frac{3log2+2log3}{2log6+log2}$$

 A) 2 B) 6 C) 1 D) 4

 C) 1

$$\Large 3log2+2log3=log2^{3}+log3^{2}$$

=$$\Large log8+log9$$

=$$\Large log \left(8 \times 9\right)=log72$$

$$\Large 2log6+log2=log6^{2}+log2$$

=$$\Large log36+log2$$

$$\Large \frac{3log2+2log3}{2log6+log2}=\frac{log72}{log72}$$

= 1

Part of solved Logarithms questions and answers : >> Elementary Mathematics >> Logarithms

Similar Questions
1). Find the value of $$\Large \frac{log16-2log2+5log3-log27}{log4+log9}$$
 A). 4 B). 1 C). 3 D). 9
2). If log3=.4771, log5=.6990, then find the value of log150
 A). 2.1761 B). 2.1671 C). 2 D). 1.1761
3). $$\Large logx^{2}+logy^{2}$$ is
 A). $$\Large log \left(x^{2}+y^{2}\right)$$ B). $$\Large 2log \left(x+y\right)$$ C). $$\Large 2log \left(xy\right)$$ D). $$\Large log\frac{x^{2}}{y^{2}}$$
4). $$\Large \left(log_{b}a \times log_{c}b \times log_{a}c\right)$$ is equal to
 A). 0 B). 1 C). abc D). a+b+c
5). If $$\Large A=\{ 1, 3, 5, 7 \},\ B=\{ 1, 2, 4, 6, 8 \},\ C=\{ 1, 3, 6, 8 \}$$ then finr $$\Large A\cap \left(B\cup C\right)$$ and $$\Large \left(A\cap B\right)\cup \left(A\cap C\right)$$
 A). $$\Large \{ 1, 3 \}$$ B). $$\Large \{ 3, 5 \}$$ C). $$\Large \{ 6, 8 \}$$ D). None of these

6). If $$\Large E=\{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \};$$ $$\Large A=\{ 1, 3, 5, 7 \},\ B=\{ 2, 4, 6, 8 \}$$ then find the value of $$\Large \left(A\cup B\right)'$$ and $$\Large A'\cap B'$$
 A). $$\Large \{ 6 \}$$ B). $$\Large \{ 9 \}$$ C). $$\Large \{ \}$$ D). None of these
7). If $$\Large A=\{ 1, 2, 3, 4 \},\ B=\{ 3, 4, 5, 6 \},\ C=\{ 6, 7, 8, 9 \}$$ then find the set $$\Large A\cap \left(B\cup C\right)$$
 A). $$\Large \{ 1, 2 \}$$ B). $$\Large \{ 2, 3 \}$$ C). $$\Large \{ 3, 4 \}$$ D). $$\Large \{ 6, 7 \}$$
8). $$\Large A=\{ 1, 2, 3, 4 \},\ B=\{ 3, 4, 5, 6 \},\ C=\{ 6, 7, 8, 9 \}$$ then find the set $$\Large A- \left(B\cup C\right)\ and\ \left(A-B\right)\cap \left(A-C\right)$$
 A). $$\Large \{ 1, 2 \}$$ B). $$\Large \{ 3, 4 \}$$ C). $$\Large \{ 6, 7 \}$$ D). $$\Large \{ 8, 9 \}$$
9). $$\Large A=\{ 4, 9, 16, 25, 36 \},\ B=\{ 9, 25, 49, 81 \},\ C=\{ 16, 81, 256 \}$$ then find $$\Large A- \left(B\cap C\right)$$
 A). $$\Large \{ 81 \}$$ B). $$\Large \{ 4, 9, 16, 25, 36 \}$$ C). $$\Large \{ 4, 36 \}$$ D). $$\Large \{ 4, 16, 36 \}$$
10). If $$\Large n \left(A\right)=6, n \left(B\right)=5, n \left(A\cap B\right)=3$$ then find $$\Large n \left(A\cup B\right)$$