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If \( \Large 7^{x}=\frac{1}{343} \), then the value of x is

A) 3
B) -3
C) \( \Large \frac{1}{3} \)
D) \( \Large \frac{1}{7} \)

Correct Answer:


B) -3

Description for Correct answer:
\( \Large 7^{x} = \frac{1}{343} = \frac{1}{7^{3}} \)

\( \Large 7^{x} = \frac{1}{7^{3}} \)

\( \Large 7^{x} = 7^{-3} \)

x = -3

[If bases are same then their power are also equal]

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

Comments

Similar Questions

1). \( \Large \frac{\frac{1}{3}.\frac{1}{3}.\frac{1}{3}+\frac{1}{4}.\frac{1}{4}.\frac{1}{4}-3\frac{1}{3}.\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{5}.\frac{1}{5}}{\frac{1}{3}.\frac{1}{3}+\frac{1}{4}.\frac{1}{4}+\frac{1}{5}.\frac{1}{5}-\left(\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{3}\right) } \) is

A). \( \Large \frac{2}{3} \)

B). \( \Large \frac{3}{4} \)

C). \( \Large \frac{47}{60} \)

D). \( \Large \frac{49}{60} \)

2). If \( \Large 0.13 \times p^{3}=13 \), then p is equal to

A). 10

B). 0.01

C). 0.1

D). 100

3). If \( \Large \frac{x}{y}=\frac{3}{4} \), the value of \( \Large \frac{6}{7}+\frac{y-x}{y+x} \) is:

A). 1

B). \( \Large \frac{2}{7} \)

C). \( \Large \frac{3}{7} \)

D). \( \Large 1\frac{3}{7} \)

4). If \( \Large x=7-4\sqrt{3} \), then \( \Large \sqrt{x}+\frac{1}{\sqrt{x}} \) is equal to:

A). 1

B). 2

C). 3

D). 4

5). If \( \Large a=\frac{\sqrt{5}+1}{\sqrt{5}-1}\ and\ b=\frac{\sqrt{5}-1}{\sqrt{5}+1} \), then the value of \( \Large \frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}} \)

A). \( \Large \frac{3}{4} \)

B). \( \Large \frac{4}{3} \)

C). \( \Large \frac{3}{5} \)

D). \( \Large \frac{5}{3} \)

6). If a=4.36, b=2.39 and c=1.97, then the value of \( \Large a^{3}-b^{3}-c^{3}-3abc \) is

A). 3.94

B). 2.39

C). 0

D). 1

7). If \( \Large \frac{3a+5b}{3a-5b}=5 \), then a:b is equal to:

A). 2:1

B). 2:3

C). 1:3

D). 5:2

8). If p:q=r:s=t:u=2:3, then \( \Large \left(mp+nr+ot\right): \left(mq+ns+ou\right) \) equals

A). 3:2

B). 2:3

C). 1:3

D). 1:2

9). If x:y=3:4, then \( \Large \left(7x+3y\right): \left(7x-3y\right) \) is equal to:

A). 5:2

B). 4:3

C). 11:3

D). 37:19

10). For what value(s) of a is \( \Large x+\frac{1}{4}\sqrt{x}+a^{2} \) a perfect square?

A). \( \Large \pm \frac{1}{18} \)

B). \( \Large \frac{1}{8} \)

C). \( \Large -\frac{1}{5} \)

D). \( \Large \frac{1}{4} \)