Đáp án + Giải thích các bước giải:
bài 1
a) 5 . 5^2 . 5^7 = 5^1 . 5^2 . 5^7 = 5^10
b) 3. 5 . 15 . 15^3 = 15^1 . 15^1 . 15^3 = 15^5
c) 2^15 : 2^11 = 2^4
d) 11^300 : 11^200 = 11^100
e) a . a^2 . a^5 = a^1 . a^2 . a^5 = a^8
g) x^10 . x^20 . x^30 = x^60
h) m^10 : m = m^15 : m^1 = m^14
k) 2^1 . 2^2 . 2^x + 1 = 2^1 . 2^2 . 2^x . 2^1 = 2^4 . 2^x = 2^x + 4
bài 2
a) x^2 = 16 b) x^2 = 81 c) ( x - 3 )^2 = 81 d) ( x + 1 )^3 = 125
-> x = 4 -> x = 9 -> x - 3 = 9 -> ( x + 1 )^3 = 5^3
-> x = 6 -> x + 1 = 5
-> x = 4
e) ( 7 - x )^3 = 216 g) ( 2x - 1 )^2 = 49 h) 2^x = 8 k) 3^x - 1 = 243
-> (7 - x )^3 = 6^3 -> ( 2x - 1 )^2 = 7^2 -> 2^x = 2^3 -> 3^x - 3^1 = 3^5
-> 7 - x = 6 -> 2x -1 = 7 -> x = 3 -> 3^x = 3^4
-> x = 1 -> 2x = 6 -> x = 4
-> x = 3
bài 3
a) 5 . 5^x + 5^1 = 625 b) 2^x . 2^x - 2^1 = 32 c) 2^x + 2^x + 2^1 = 48
-> 5^1 . 5^x + 5^1 = 5^4 2^x . 2^x - 2^1 = 2^5 -> 2^x + 2^x + 2^1 = 2^5 + 2^4
-> 5^2 . 5^x = 5^4 -> 2^x . 2^x = 2^4 -> 2^x + 2^x = 2^4 + 2^4
-> 5^x = 5^2 -> 2^x = 2^2 -> 2^x = 2^4
-> x = 2 -> x = 2 -> x = 4
