Let’s go through each problem one by one. We’ll rewrite logarithmic equations as exponential, and vice versa — just like switching between two ways of saying the same thing.
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Rewrite each equation in exponential form.
1) log₆ 36 = 2
→ This means: “6 raised to what power gives 36?” → Answer is 2.
So exponential form:
6² = 36
2) log₂₈₉ 17 = ½
→ “289 raised to what power gives 17?” → Answer is ½ (square root).
Exponential form:
289^(½) = 17
3) log₁₄ (1/196) = -2
→ “14 raised to what power gives 1/196?” → Negative exponent means reciprocal.
14⁻² = 1/(14²) = 1/196 → So:
14⁻² = 1/196
4) log₃ 81 = 4
→ “3 raised to what power gives 81?” → 3×3×3×3 = 81 → So:
3⁴ = 81
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Rewrite each equation in logarithmic form.
5) 64^(½) = 8
→ “What power do I raise 64 to, to get 8?” → That’s ½.
Logarithmic form:
log₆₄ 8 = ½
6) 12² = 144
→ “What power do I raise 12 to, to get 144?” → That’s 2.
Logarithmic form:
log₁₂ 144 = 2
7) 9⁻² = 1/81
→ “What power do I raise 9 to, to get 1/81?” → That’s -2.
Logarithmic form:
log₉ (1/81) = -2
8) (1/12)² = 1/144
→ “What power do I raise 1/12 to, to get 1/144?” → That’s 2.
Logarithmic form:
log_(1/12) (1/144) = 2
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Rewrite each equation in exponential form.
9) logₐ (15/16) = c
→ “a raised to what power gives 15/16?” → Answer is c.
Exponential form:
aᶜ = 15/16
10) logᵥ a = 4
→ “v raised to what power gives a?” → Answer is 4.
Exponential form:
v⁴ = a
11) log_(7/4) x = y
→ “(7/4) raised to what power gives x?” → Answer is y.
Exponential form:
(7/4)ʸ = x
12) log₂ v = u
→ “2 raised to what power gives v?” → Answer is u.
Exponential form:
2ᵘ = v
13) logₐ v = -16
→ “a raised to what power gives v?” → Answer is -16.
Exponential form:
a⁻¹⁶ = v
14) log_y z = -8
→ “y raised to what power gives z?” → Answer is -8.
Exponential form:
y⁻⁸ = z
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Rewrite each equation in logarithmic form.
15) a⁻¹⁴ = v
→ “What power do I raise a to, to get v?” → That’s -14.
Logarithmic form:
logₐ v = -14
16) bˣ = a
→ “What power do I raise b to, to get a?” → That’s x.
Logarithmic form:
log_b a = x
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Final Answer:
1) 6² = 36
2) 289^(½) = 17
3) 14⁻² = 1/196
4) 3⁴ = 81
5) log₆₄ 8 = ½
6) log₁₂ 144 = 2
7) log₉ (1/81) = -2
8) log_(1/12) (1/144) = 2
9) aᶜ = 15/16
10) v⁴ = a
11) (7/4)ʸ = x
12) 2ᵘ = v
13) a⁻¹⁶ = v
14) y⁻⁸ = z
15) logₐ v = -14
16) log_b a = x
Parent Tip: Review the logic above to help your child master the concept of logarithm worksheet kuta.
