Logarithms | MCQs

Explanation

The logarithm of any number to itself as base is 1.

This is because log(a)/a = 1, where 'a' is any number.

Explanation

Explanation

Using the change of base formula:

log_b^a / log_b^d = log_d^a

Explanation

Loga (m × n) = Loga m + Loga n.

This is a logarithmic property: the log of a product is the sum of the logs.

Explanation

Answer:

Log1 

When two logs are being subtracted from each other, it is the same thing as dividing two logs together. Remember that to use this rule, the logs must have the same base in this case.

Explanation

1/log3(60) + 1/log4(60) + 1/log5(60)

= log60(3) + log60(4) + log60(5) (using the change of base formula)

= log60(3×4×5) (using the product rule of logarithms)

= log60(60)

= 1 (since log60(60) is equal to 1)

So the correct answer is: 1

Explanation

Given:

log₈₁ 9 = x

We can rewrite this in exponential form:

81^x = 9

Since 81 = 9², we can rewrite:

(9²)^x = 9

9^(2x) = 9¹

Equating the exponents:

2x = 1

x = 1/2

x = 0.5

Explanation

Given logx (4/9) = 2

This can be rewritten as:

x² = 4/9

Taking the square root of both sides:

x = ±√(4/9)

x = ±2/3

Since the base of a logarithm is typically positive, we consider x = 2/3.

Explanation

Given:

logx 0.25 = 2

This can be rewritten in exponential form:

x² = 0.25

Taking the square root of both sides:

x = √0.25

x = 0.5

Explanation

The number 0.00435 is less than 1, so the logarithm will have a negative characteristic.

Count digits after the decimal up to the first non-zero digit (2 digits: "00"), then apply:

Characteristic = – (number of zeros + 1) = – (2 + 1) = –3