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If $f (x) = \log_{2} x + \log_{2} (x^{2} - 1) - \log_{2} (x + 1)$ then

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Important Questions on Quantity

MEDIUM

Mathematics>Algebra>Quantity>Solving Exponential Equations

If $\log 3^{x + 4} = \log 729$ then the value of $x$ will be

MEDIUM

Mathematics>Algebra>Quantity>Solving Exponential Equations

Let

n

be the smallest positive integer such that

1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n} \geq 4

. Which one of the following statements is true?

EASY

Mathematics>Algebra>Quantity>Solving Exponential Equations

\log_{e} (y^{2}) = \tan (\frac{1}{x}),

then

y =

EASY

Mathematics>Algebra>Quantity>Solving Exponential Equations

\log_{0.01} (10, 000) = x

; Find the value of

x

MEDIUM

Mathematics>Algebra>Quantity>Solving Exponential Equations

x + \log_{10} (1 + 2^{x}) = x \log_{10} 5 + \log_{10} 6,

then the value of

x

HARD

Mathematics>Algebra>Quantity>Solving Exponential Equations

Let

S

be the sum of the digits of the number

15^{2} \times 5^{18}

in base

10

. Then,

EASY

Mathematics>Algebra>Quantity>Solving Exponential Equations

\log_{8} x + \log_{4} x + \log_{2} x = 11, x =

EASY

Mathematics>Algebra>Quantity>Solving Exponential Equations

For

0 < m < 1

, which one of the following is correct?

EASY

Mathematics>Algebra>Quantity>Solving Exponential Equations

2 \log (x + 1) - \log (x^{2} - 1) = \log 2,

then

x =

HARD

Mathematics>Algebra>Quantity>Solving Exponential Equations

The solution set of the inequality

\log_{\sin (π / 3)} (x^{2} - 3 x + 2) \geq 2

MEDIUM

Mathematics>Algebra>Quantity>Solving Exponential Equations

Let

x, y

be real numbers such that

x > 2 y > 0

and

2 \log (x - 2 y) = \log x + \log y

. Then the possible value(s) of

\frac{x}{y}

HARD

Mathematics>Algebra>Quantity>Solving Exponential Equations

\log_{(3 x - 1)} (x - 2) = \log_{(9 x^{2} - 6 x + 1)} (2 x^{2} - 10 x - 2),

then

x

equals-

MEDIUM

Mathematics>Algebra>Quantity>Solving Exponential Equations

Let

n

be a positive integer such that

\log_{2} \log_{2} \log_{2} \log_{2} \log_{2} (n) < 0 < \log_{2} \log_{2} \log_{2} \log_{2} (n)

. Let

l

be the number of digits in the binary expansion of

n

. Then the minimum and the maximum possible values of

l

are

MEDIUM

Mathematics>Algebra>Quantity>Solving Exponential Equations

The number of solution pairs

(x, y)

of the simultaneous equations

\log_{1 / 3} (x + y) + \log_{3} (x - y) = 2

and

2 y^{2} = 512^{x + 1}

HARD

Mathematics>Algebra>Quantity>Solving Exponential Equations

The real roots of the equation

7^{\log_{7} (x^{2} - 4 x + 5)} = x - 1

are

HARD

Mathematics>Algebra>Quantity>Solving Exponential Equations

The least integer

a

, for which

1 + \log_{5} (x^{2} + 1) \leq \log_{5} (a x^{2} + 4 x + a)

is true for all

x \in R

is-

EASY

Mathematics>Algebra>Quantity>Solving Exponential Equations

Which of the following is negative ?

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Mathematics>Algebra>Quantity>Solving Exponential Equations

Solve

\log_{3} (5 x - 1) > 0

EASY

Mathematics>Algebra>Quantity>Solving Exponential Equations

\log_{\frac{1}{\sqrt{2}}} \sin x > 0, x \in [0, 4 π]

, then the number of values of

x

, which are integral multiples of

\frac{π}{4}

is.

MEDIUM

Mathematics>Algebra>Quantity>Solving Exponential Equations

Set of all the values of

x

satisfying the inequality

\log_{x + \frac{1}{x}} (\log_{2} \frac{x - 1}{x + 2}) > 0

If fx=log2x+log2x2-1-log2x+1 then

Important Questions on Quantity

Learn and Prepare for any exam you want !

If $f (x) = \log_{2} x + \log_{2} (x^{2} - 1) - \log_{2} (x + 1)$ then