Ցուցչային հավասարման բանաձև՝

a^x = b b </ 0 = > ◯
2^x = 32
2^x = 2⁵
x = 5

Առաջադրանքներ՝

դ) (1/4)^x = 16
1/4 = 4^-1
(4 — 1)^x = 4²
4^-x = 4²
-x = 2
x = -2

ա) 3^x+2 = 81
3^x+2 = 3⁴
x + 2 = 4
x = 4 — 2 = 2

գ) (√3)^{x — 5} = 27
(√3)^{x — 5} = 3³
(3^1/2)^{x — 5} = 3³
1/2 * x — 5 = x-5/2
3^{x — 5/2} = 3³
x — 5/2 = 3/1
x — 5 = 6
x = 6 + 5 = 11

զ) (0,125)^3-x = 2√2
2√2 = 2¹ * 2^1/2 = 2^{1 + 1/2} = 2^3/2
125/1000 = 1/8 = 1/2³ = 2^-3
(2^-3)^3-x = 2^3/2
-3 * 3 — x = -9 + 3x
-9 + 3x = 3/2
3x = 3/2 + 9 = 3 + 18/2 = 21/2
x = 21/2 * 3 = 21/6 = 7/2

ա) 6^3x+2 = 6^{2x + 7}
3x + 2 = 2x + 7
3x — 2x = 7 — 2
x = 5

բ) 5^4x+1 = (0,2)^x-6
0,2 = 2/10 = 1/5 = 5^-1
5^4x+1 = (5^-1)^x-6
-1 * (x — 6) = -x + 6
4x + 1 = -x + 6
5x = 5
x = 1