Logarithms
ICSE · Class 9 · Mathematics
Flashcards for Logarithms — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedWhat is a logarithm? Define logarithm with an example.
Answer
A logarithm is the power to which a base must be raised to get a specific number. If a^b = c, then log_a c = b (read as 'log of c to the base a equals b'). Example: Since 2^3 = 8, we can write log_2 8…
Convert the exponential form 5^3 = 125 to logarithmic form.
Answer
log_5 125 = 3 (logarithm of 125 to the base 5 equals 3)…
Convert the logarithmic form log_2 16 = 4 to exponential form.
Answer
2^4 = 16…
What is the value of log_a 1 for any positive base a ≠ 1?
Answer
log_a 1 = 0. This is because a^0 = 1 for any positive number a. Examples: log_5 1 = 0, log_10 1 = 0.
What is the value of log_a a for any positive base a ≠ 1?
Answer
log_a a = 1. This is because a^1 = a. Examples: log_5 5 = 1, log_10 10 = 1.
State the First Law of Logarithms (Product Law).
Answer
log_a(m × n) = log_a m + log_a n. The logarithm of a product equals the sum of logarithms of the factors. Example: log_10(2 × 5) = log_10 2 + log_10 5.
State the Second Law of Logarithms (Quotient Law).
Answer
log_a(m/n) = log_a m - log_a n. The logarithm of a quotient equals the difference of logarithms. Example: log_10(8/2) = log_10 8 - log_10 2.
State the Third Law of Logarithms (Power Law).
Answer
log_a(m^n) = n log_a m. The logarithm of a power equals the exponent times the logarithm of the base. Example: log_10(2^3) = 3 log_10 2.
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