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If \( \Large y = 2^{\frac{1}{logx}\left(8\right)} \), then x is equal to:

A) y
B) \( \Large y^{2} \)
C) \( \Large y^{3} \)
D) none of these

Correct Answer:



C) \( \Large y^{3} \)

Description for Correct answer:
\( \Large y = 2^{\frac{1}{log}x \left(8\right) } \)

=> \( \Large y = 2 ^{log 8x} => y = 2^{log 2\sqrt[3]{x}} \)

=> \( \Large x = y^{3} \)

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

Comments

Similar Questions

1). If \( \Large log_{05} \sin x = 1 - log_{05} \cos x \), then number of solution of \( \Large x ? \left[ -2 \pi , 2 \pi \right] \) is:

A). 1

B). 2

C). 3

D). 4

2). If a, b, c are in GP. then \( \Large log ax^{x}, log_{bx}x, log_{cx}x \) are in:

A). GP

B). HP

C). AP

D). none of these

3). Consider the following statements:
1. Solution of the inequality \( \Large log_{5} \left(x^{2}-11x+43\right)<2 \) is (0, 2)
2. If \( \Large [x - 1]^{ \left(log_{3}x^{2} - 2Logx^{9}\right)} = \left(x - 1\right)^{7} \), then x is 2 and 81.
Which of these is/are correct?

A). only(1)

B). only 2

C). both of these

D). none of these

4). \( \Large log \cos x \sin x \ge 2 \) and \( \Large x \epsilon \left[ 0, 3 \pi \right] \), then \( \Large \sin x \) lines in the interval:

A). \( \Large \left[ 0, \frac{1}{2} \right] \)

B). \( \Large \left[\frac{\sqrt{5}-1}{2}, 1 \right] \)

C). \( \Large \left[ 0, \frac{\sqrt{5}-1}{2} \right] \)

D). none of these

5). If \( \Large log_{2} x + log_{2} y \ge 6 \), then the least value of \( \Large \left(x + y\right) \) is

A). 4

B). 9

C). 16

D). 32

6). If \( \Large 4^{log_{3}\frac{31}{2}} + 9^{log2^{2}} = 10^{log_{x}83} \), (x belongs to R), then x is:

A). 4

B). 9

C). 10

D). none of these

7). Which of the following is not true?

A). \( \Large \frac{1}{log_{3} \pi } + \frac{1}{log_{4} \pi }>2 \)

B). \( \Large log_{3}5 \)

C). \( \Large \sqrt{8x} = \frac{10}{3} => x = 16 \)

D). \( \Large log_{x} \left(a^{2}+1\right)<0 \), (a?0) then 0

8). If \( \Large y = \frac{1}{a^{1-log ax}} \) and \( \Large z = \frac{1}{a^{1+log_{a}y}} \) then x is equal to:

A). \( \Large \frac{1}{a^{1+log_{a}z}} \)

B). \( \Large \frac{1}{a^{z+log_{a}z}} \)

C). \( \Large \frac{1}{a^{1-log_{a}z}} \)

D). none of these

9). The least value of n in order that the sum of first n terms of an infinite series \( \Large 1 + \frac{3}{4} + \left(\frac{3}{4}\right)^{2} + \left(\frac{3}{4}\right)^{3}+ .... \) should differ from the sum of the series by less then \( \Large 10^{-6} \) is
[\( \Large\ Given\ log_{10}2=0.30103, log_{10}3=0.47712 \)]

A). 14

B). 27

C). 53

D). 57

10). Solution of the equation \( \Large x log^{x^{2}} = log3 \left(x+y\right) \) and \( \Large x^{2}+y^{2} = 65 \) is:

A). x = 8, y = 1

B). x = 1, y = 8

C). (x=8, y=1); (x=1, y=8)

D). none of the above