Indices, Surds, Logarithms(Lowersixth Science II Mathematics)

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Challenging logarithm and index problems.

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Indices, Surds, Logarithms(Lowersixth Science II Mathematics)


Froggy Jumps Indices, Surds, Logarithms(Lowersixth Science II Mathematics)Online version Challenging logarithm and index problems. by YAKILI LMS 1 What is the rationalized form of 3/√5? a √5/5 b 3√5/5 c 5/3√5 2 Simplify log_b(b^3) with base b. a b^3 b log(b) c 3 3 If log2(8) = x, what is x? a 3 b 2 c 4 4 Which rule is used for log(ab)? a log a - log b b log(a/b) c log a + log b 5 Solve log10(x) = 2. a x = 100 b x = 2 c x = -100 6 The inverse of f(x) = log_b(x) is: a x^b b log_b(x) c f^{-1}(x) = b^x 7 If log_3(x) = 4, what is x? a 12 b 64 c 81 8 Laws of logarithms: log(a^n) = ? a a^n b n log a c log(an) 9 Solve for x: log(x) = log(7) -> x = ? a 1 b 0 c 7 10 Combine: log(4) + log(9) = a log(45) b log(13) c log(36) 11 What is log base 2 of 16? a 8 b 2 c 4 12 If log_a(b) = c, then b = a^c. True or false? a True b Depends on a c False 13 Find x from log_5(x^2) = 2. a x = -25 b x = 5 or x = -5 c x = 25 14 Solve: log_2(x) + log_2(x-1) = 3. a x = 3 b x = 5 c x = 4 15 Rationalize: 6/(√2 + √8). a 3/√2 b √2/2 c 2/√2 16 Common log: log10(0.01) = a 0 b 2 c -2 17 If log_2(x) = log_2(3) then x = a 1/3 b 3 c 6 18 Solve simultaneous: log_a(x) = 2 and log_a(y) = 3. a x = a^2, y = a^3 b x = a^2y = a^3 c x = a^3, y = a^2 19 Inverse function: if f(x)=log(x), f^{-1}(x) = a 10^x b log(x) c e^x 20 What is log_b(1)? a 0 b 1 c b 21 Solve: log_4(x^3) = 6. a x = 64 b x = 4 c x = 4^2 = 16 22 If log_b(M) = p and log_b(N) = q, then log_b(MN) = a p-q b pq c p+q 23 Rationalize: 7/ (3√7). a √7/3 b 3√7/7 c 7/3 24 Which operation uses log(a) - log(b) = log(a/b)? a Quotient rule b Product rule c Power rule 25 If log_2(x) = 5, then x = a 10 b 32 c 25 26 Compute log_10(1000). a -3 b 3 c 0 27 Solve: log_3(x^2) = 4. a x = 3^2 = 9 or x = -9 b x = 12 c x = 64 28 Logarithmic form of e^2 = ? a ln(e^2) = 2 b log_e(2) = 2 c ln(2) = e^2 29 What is log_b(b) equal to? a b b 1 c 0 30 Solve: log_2(x) - log_2(x-1) = 1. a x = 2 b x = 3 c x = 4 31 Inverse: If f(x)=ln(x), f^{-1}(x) = a x^e b e^x c ln(x) 32 Rationalize: 8/(√3 - 1). a 8√3-8 b 4√3+4 c 8(√3+1)/(2) 33 Compute log_5(25). a 5 b 2 c -2 34 If log_a(b) = c, then a^c = a c b a c b 35 Solve: log_6(x) = log_6(2x). a x = 0 or x = ∞ (no finite) b x = 1/3 c x = 2 36 Logarithm identity: log_b(1) = a 0 b b c 1 37 Find the domain of log(x-2). a x > 2 b x < 2 c x ≠ 2 38 If log_2(x) = 3 and log_2(y) = 4, log_2(xy) = a 7 b 1 c 12 39 Rationalize: (a√b)/(√b) = ? a ab b a c √b 40 What is log_7(1/7)? a 0 b -1 c 1 41 Solve: log_10(x^2) = 4. a x = ±100 b x = 1000 c x = 10 42 Logarithm property: log_b(a^k) = a log(a) / log(b) b k log_b(a) c log_b(a+k) 43 If log_2(x) = 1/2, x = a 1/2 b 2 c √2 44 Solve: log_3(x) + log_3(x-1) = 1. a x = 3 b x = 3/2 c x = 9/2 45 What is the common logarithm of 100? a 2 b 1 c -2 46 Solve the system: x + y = 3 and log10(x) = y. Find x and y. a x ≈ 2.60, y ≈ 0.40 b x ≈ 1.40, y ≈ 1.60 c x ≈ 3.00, y ≈ 0.00 47 If x^2 = y and x + y = 5, what are x and y? a x ≈ 3.00, y ≈ 2.00 b x ≈ 1.79, y ≈ 3.21 c x ≈ 2.50, y ≈ 2.50 48 If y = x^3 and x + y = 6, what are x and y? a x ≈ 1.00, y ≈ 5.00 b x ≈ 1.63, y ≈ 4.37 c x ≈ 2.00, y ≈ 4.00 49 Solve y = log2(x) and x + y = 5 for x and y. a x ≈ 3.28, y ≈ 1.72 b x ≈ 4.00, y ≈ 1.00 c x ≈ 2.50, y ≈ 2.50 50 If y = log10(x) and x + y = 4, find x and y. a x ≈ 1.50, y ≈ 2.50 b x ≈ 3.28, y ≈ 0.72 c x ≈ 2.00, y ≈ 2.00

Indices, Surds, Logarithms(Lowersixth Science II Mathematics)

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Indices, Surds, Logarithms(Lowersixth Science II Mathematics)Online version

by YAKILI LMS

What is the rationalized form of 3/√5?

Simplify log_b(b^3) with base b.

If log2(8) = x, what is x?

Which rule is used for log(ab)?

Solve log10(x) = 2.

The inverse of f(x) = log_b(x) is:

If log_3(x) = 4, what is x?

Laws of logarithms: log(a^n) = ?

Solve for x: log(x) = log(7) -> x = ?

Combine: log(4) + log(9) =

What is log base 2 of 16?

If log_a(b) = c, then b = a^c. True or false?

Find x from log_5(x^2) = 2.

Solve: log_2(x) + log_2(x-1) = 3.

Rationalize: 6/(√2 + √8).

Common log: log10(0.01) =

If log_2(x) = log_2(3) then x =

Solve simultaneous: log_a(x) = 2 and log_a(y) = 3.

Inverse function: if f(x)=log(x), f^{-1}(x) =

What is log_b(1)?

Solve: log_4(x^3) = 6.

If log_b(M) = p and log_b(N) = q, then log_b(MN) =

Rationalize: 7/ (3√7).

Which operation uses log(a) - log(b) = log(a/b)?

If log_2(x) = 5, then x =

Compute log_10(1000).

Solve: log_3(x^2) = 4.

Logarithmic form of e^2 = ?

What is log_b(b) equal to?

Solve: log_2(x) - log_2(x-1) = 1.

Inverse: If f(x)=ln(x), f^{-1}(x) =

Rationalize: 8/(√3 - 1).

Compute log_5(25).

If log_a(b) = c, then a^c =

Solve: log_6(x) = log_6(2x).

Logarithm identity: log_b(1) =

Find the domain of log(x-2).

If log_2(x) = 3 and log_2(y) = 4, log_2(xy) =

Rationalize: (a√b)/(√b) = ?

What is log_7(1/7)?

Solve: log_10(x^2) = 4.

Logarithm property: log_b(a^k) =

If log_2(x) = 1/2, x =

Solve: log_3(x) + log_3(x-1) = 1.

What is the common logarithm of 100?

Solve the system: x + y = 3 and log10(x) = y. Find x and y.

If x^2 = y and x + y = 5, what are x and y?

If y = x^3 and x + y = 6, what are x and y?

Solve y = log2(x) and x + y = 5 for x and y.

If y = log10(x) and x + y = 4, find x and y.