Topic 1.5Math AI SL SL16 flashcards

Exponents and logarithms

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Card 1 of 161.5.1

1.5.1

Question

What is the law for multiplying powers with the same base?

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All Flashcards in Topic 1.5

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1.5.14 cards

Card 1formula

Question

What is the law for multiplying powers with the same base?

Answer

a^m × a^n = a^(m+n).

💡 Hint

Add the powers

Card 2formula

Question

What is the law for dividing powers with the same base?

Answer

a^m ÷ a^n = a^(m-n).

💡 Hint

Subtract the powers

Card 3concept

Question

What does a negative exponent mean?

Answer

a^(-n) = 1/a^n. It means reciprocal, not negative answer.

💡 Hint

Think reciprocal

Card 4example

Question

Simplify (x^3)^2.

Answer

x^6. Multiply the powers: 3 × 2 = 6.

💡 Hint

Power of a power

1.5.24 cards

Card 5definition

Question

What does log_a b = c mean?

Answer

It means a^c = b. A logarithm gives the exponent needed on the base.

💡 Hint

Log = exponent

Card 6example

Question

What is log_2 8?

Answer

3, because 2^3 = 8.

💡 Hint

Ask what power of 2 gives 8

Card 7example

Question

Rewrite 10^4 = 10000 in log form.

Answer

log_10 10000 = 4.

💡 Hint

Base stays 10

Card 8definition

Question

What does plain log usually mean on the calculator?

Answer

It usually means log base 10.

💡 Hint

Common log

1.5.34 cards

Card 9formula

Question

What is the product law of logarithms?

Answer

log_a(xy) = log_a x + log_a y.

💡 Hint

Product becomes addition

Card 10formula

Question

What is the quotient law of logarithms?

Answer

log_a(x/y) = log_a x - log_a y.

💡 Hint

Division becomes subtraction

Card 11formula

Question

What is the power law of logarithms?

Answer

log_a(x^n) = n log_a x.

💡 Hint

Bring the power down

Card 12concept

Question

Why is log(x + y) = log x + log y wrong?

Answer

Because the product law works for multiplication, not addition.

💡 Hint

Addition is the trap

1.5.44 cards

Card 13example

Question

How do you solve 2^(x+1) = 16?

Answer

Rewrite 16 as 2^4, then set exponents equal: x + 1 = 4, so x = 3.

💡 Hint

Use a common base first

Card 14concept

Question

How do you solve 3^x = 20?

Answer

Use logs: x = log(20)/log(3).

💡 Hint

Bring the exponent down

Card 15example

Question

Solve log_2 x = 5.

Answer

x = 32, because x = 2^5.

💡 Hint

Rewrite as a power statement

Card 16concept

Question

What restriction must hold in a logarithm like log x?

Answer

The input must be positive: x > 0.

💡 Hint

Positive inputs only

Topic 1.5 study notes

Full notes & explanations for Exponents and logarithms

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