What is the value of x if log3x + log9x + log27x + log81x = 25/4?a)9b)27c)81d)None of thCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Solution:

The given expression is:

log3x log9x log27x log81x = 25/4

We know that:

loga(b) = logc(b) / logc(a)

Using this property, we can write:

log3x = log9x / log93

log9x = log27x / log93

log27x = log81x / log93

Substituting these values in the given expression, we get:

log9x / log93 + log27x / log93 + log81x / log93 + log3x = 25/4

Simplifying this expression, we get:

log3x (1 + 3 + 9 + 81) = 25/4 log93

log3x (94) = 25/4 (log93)

log3x = 25/4 (log93) / 94

log3x = 25/4 (1/2)

log3x = 25/8

Using the property loga(b) = c, we can write:

3^(25/8) = x

Simplifying this expression, we get:

x = 27

Therefore, the value of x is 27, which is given in option B.

Similar Quant Doubts

Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1)F(x–2)F(x–3)F(x–4) for all x ≥ 0.Given the values of If F (83) = 81 and F(77) = 9, then the value of F(81) equals to

If 2 [log (x + y) - log 5] = logx + logy, then what is the value of x2 + y2?

What is the value of P if log,2. logp625 = log10 16.log10?

A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the integer values of x and f(1) + f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?

The value of a machine depreciates 10% annually. If its present value is Rs. 4000, its value 2 years hence will be

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company