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Explanation & Answer

Attached.
1- 𝑙𝑜𝑔3 2187 = 3
4
2- 83 = 16
3- 𝑙𝑜𝑔3 5 =
4- 𝑙𝑜𝑔2
1
64
𝑙𝑜𝑔10 5
𝑙𝑜𝑔10 3
=
= 𝑙𝑜𝑔2 64
log 5
log 3
−1
= 𝟏. 𝟒𝟔𝟒𝟗𝟕 ≅ 𝟏. 𝟒𝟔𝟓𝟎
= 𝑙𝑜𝑔2 (26 )−1 = 𝑙𝑜𝑔2 2−6 = −6 𝑙𝑜𝑔2 2 = −𝟔
5- 𝑙𝑜𝑔4 21 = 𝑙𝑜𝑔4 (3 × 7) = 𝑙𝑜𝑔4 3 + 𝑙𝑜𝑔4 7 = 0.7925 + 1.4037 =
𝟐. 𝟏𝟗𝟔𝟐
6- 𝑙𝑜𝑔4 (7/12) = 𝑙𝑜𝑔4 7 − 𝑙𝑜𝑔4 12 = 𝑙𝑜𝑔4 7 − 𝑙𝑜𝑔4 (3 × 4) =
𝑙𝑜𝑔4 7 − (𝑙𝑜𝑔4 3 + (𝑙𝑜𝑔4 4) = 1.4037 − (0.7925 + 1) =
−𝟎. 𝟑𝟖𝟖𝟖
7- 272𝑝+1 = 34𝑝−1
(33 )2𝑝+1 = 34𝑝−1
33(2𝑝+1) = 34𝑝−1
36𝑝+3 = 34𝑝−1
6p+3 = 4p-1
2p = -4
P= -2
8- 𝑙𝑜𝑔𝑚 144 = −2 converting to the exponential form
144 = 𝑚−2
1
144 = ( )2 Taking ...
