Logarithms

Play an AI-generated podcast conversation about this lesson

What is the condition on 'a' for y = loga x to be defined?

Any positive real number ≠ 1 (correct)

Any number

Any positive real number

Any positive real number > 1

What is the value of x in the equation 2^(2x) = 32^(5/4)?

3.6 (correct)

5.6

None of these

4.5

Which of the following properties of logarithms is true?

loga b = logb a

loga b.logb a = 1 (correct)

loga b.logc a = logc b

loga b.logb c = loga c

What is the value of loga (mn) if m and n are arbitrary positive numbers?

loga m + loga n Signup and view all the answers

What can be said about the number log2 7?

It is an irrational number Signup and view all the answers

What is the logarithm of a given number to a given base?

The index of the power to which the base must be raised in order to equal the given number Signup and view all the answers

What is the range of the logarithmic function f(x) = loga x, a > 0, a ≠ 1?

R Signup and view all the answers

What is the logarithmic identity that states a^(loga N) = N?

Fundamental logarithmic identity Signup and view all the answers

If the characteristic of log10 N is -n, then how many zeros are there after the decimal part of N?

n-1 Signup and view all the answers

What is the logarithmic function called when the base is e?

Napierian logarithmic function Signup and view all the answers

If log₇(2) = m, then log₄₉(28) is equal to?

2(1 + 2m) Signup and view all the answers

If logₑ(a + b) = logₑ(a) + logₑ(b), then what is the relation between a and b?

a + b = ab Signup and view all the answers

If log₁₀(3) = 0.477, then the number of digits in 3⁴⁰ is?

20 Signup and view all the answers

What is the correct order of the logarithms in increasing order for a given number α?

log₁₀(α), logₑ(α), log₂(α), log₃(α) Signup and view all the answers

If y = 3⁴⁰, then what is the value of log(y)?

19.08 Signup and view all the answers

If logₐ(m) = logₐ(n) and a ≠ 1, then what can be concluded about m and n?

m = n Signup and view all the answers

If logₐ(x) = p and logₐ(y) = q, then what is the value of logₐ(xy)?

p + q Signup and view all the answers

Solve for x in the equation log₂(x) = 3/2.

√(2³) Signup and view all the answers

If logₐ(b) = c and logₑ(d) = 1/c, then what is the value of logₑ(b)?

d Signup and view all the answers

If a^(logₐ(m)) = m, then what is the value of m^(logₘ(a))?

a Signup and view all the answers

What is the value of loga N if a^x = N and a^y = 1/N?

-x Signup and view all the answers

If the logarithm of a number is 2.5, then what is the value of the number?

10^2.5 Signup and view all the answers

What is the value of loga MN if loga M = x and loga N = y?

x + y Signup and view all the answers

If loga N = 2, then what is the value of log(a^2) N?

4 Signup and view all the answers

What is the value of loga (1/N) if loga N = x?

-x Signup and view all the answers

If logₑ(x) + logₑ(y) = logₑ(z), then what is the relationship between x, y, and z?

xy = z Signup and view all the answers

Solve for x in the equation log₂(x) = 2log₂(3) + log₂(4)

12 Signup and view all the answers