Problem 1 :
Solve for x :
Problem 2 :
Solve for y :
Problem 3 :
Solve for z :
logz8√2 = 7
Problem 4 :
Solve for k :
-3 = logk0.001
Problem 5 :
Solve for x :
log5[5log3(x)] = 2
Problem 6 :
Solve for m :
m + 2log27(9) = 0
Problem 7 :
If 2log(y) = 4log(3), then find the value of y.
Problem 8 :
If 3p is equal to log(0.3) to the base 9, then find the value of p.
Problem 9 :
Solve for r :
Problem 10 :
Solve for q :
Problem 11 :
Solve for v :
log4(v + 4) + log48 = 2
Problem 12 :
Solve for w :
log6(w + 4) - log6(w - 1) = 1
Problem 13 :
Solve for g :
Problem 14 :
Solve for x :
81√x = log2(512)
1. Answer :
Convert it to exponential form.
2. Answer :
Convert it to exponential form.
3. Answer :
logz8√2 = 7
Convert it to exponential form.
125√5 = z7
2 ⋅ 2 ⋅ 2 ⋅ √2 = x7
Each 2 can be expressed as (√2 ⋅ √2).
Then,
√2 ⋅ √2 ⋅ √2 ⋅ √2 ⋅ √2 ⋅ √2 ⋅ √2 = x7
√27 = x7
Because the exponents are equal, bases can be equated.
x = √2
4. Answer :
-3 = logk0.001
Convert it to exponential form.
k-3 = 0.001
Take reciprocal on both sides.
k3 = 1000
k3 = 103
Because the exponents are equal, bases can be equated.
k = 10
5. Answer :
log5[5log3(x)] = 2
Convert it to exponential form.
5log3(x) = 52
5log3(x) = 25
Divide both sides by 5.
log3(x) = 5
Convert it to exponential form.
x = 35
x = 243
6. Answer :
m + 2log27(9) = 0
m = -2log27(9)
x = log27(9-2)
Convert it to exponential form.
27x = 9-2
(33)x = (32)-2
33x = 3-4
Because the bases are equal, exponents can be equated.
3x = -4
7. Answer :
2log(y) = 4log(3)
Divide each side by 2.
log(y) = 2log(3)
log(y) = log(32)
log(y) = log(9)
y = 9
8. Answer :
From the information given, we have
3p = log9(0.3)
Solve for p.
9. Answer :
7r - 4 = 5(r + 2)
7r - 4 = 5r + 10
2r - 4 = 10
2r = 14
r = 7
10. Answer :
q = 31
q = 3
11. Answer :
log4(v + 4) + log48 = 2
log4[8(v + 4)] = 2
log4(8v + 32) = 2
8v + 32 = 42
8v + 32 = 16
8v = -16
v = -2
12. Answer :
log6(w + 4) - log6(w - 1) = 1
w + 4 = 6(w - 1)
w + 4 = 6w - 6
-5w + 4 = -6
-5w = -10
w = 2
13. Answer :
log2(g) = 1
g = 21
g = 2
14. Answer :
81√x = log2(512)
81√x = log2(29)
81√x = 9log2(2)
(92)√x = 9(1)
92√x = 91
2√x = 1
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