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Fundamental Laws of Logarithms

If logxlog4lo...

Question

If ${log}_{x} ({log}_{4} ({log}_{x} (5 x^{2} + 4 x^{3}))) = 0$ , then the value of $x$ is

A

2

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B

3

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C

4

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D

5

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Solution

The correct option is D $5$
${log}_{4} ({log}_{x} (5 x^{2} + 4 x^{3})) = 1$
$\Rightarrow {log}_{x} (5 x^{2} + 4 x^{3}) = 4$
$\Rightarrow 5 x^{2} + 4 x^{3} - x^{4} = 0$
$\Rightarrow x^{2} - 4 x - 5 = 0 (∵ x \neq 0) \Rightarrow (x - 5) (x + 1) = 0$
$∴ x = 5 (∵ x \neq - 1)$

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Similar questions

{log}_{x} ({log}_{4} ({log}_{x} (5 x^{2} + 4 x^{3}))) = 0

, then the value of

x

x = 1 + \sqrt{2}

, then what is the value of

x^{4} - 4 x^{3} + 4 x^{2}

x = \frac{\sqrt{3} + 1}{2}

, then the value of

4 x^{3} + 2 x^{2} - 8 x + 7

f (x)

g (x)

be two function satisfying

f (x^{2}) + g (4 - x) = 4 x^{3}, g (4 - x) + g (x) = 0

, then the value of

\int_{- 4}^{4} f (x^{2}) d x

f (x) = 4 x^{3} - x^{2} - 2 x + 1

g (x) = [\begin{matrix} M i n f (t) : 0 \leq t \leq x; & 0 \leq x \leq 1 3 - x; & 1 < x \leq 2 \end{matrix}]

g (\frac{1}{4}) + g (\frac{3}{4}) + g (\frac{5}{4})

has the value equal to

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Fundamental Laws of Logarithms

Standard XIII Mathematics

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