3×2^x+2-5×2^x+1-2^x=2
(3×2^2-5×2-1)×2^x=2^1
(12-10-1)×2^x=2^1
1×2^x=2^1
2^x=2^1
x=1
5^x+2-2×5^x+1-12×5^x=375
(5^2-2×5-12)×5^x=375
(25-10-12)×5^x=375
3×5^x=375
5^x=125
5^x=5^3
x=3
2^x×3^x+1=108
2^x×3^x×3=108
(2×3)^x×3=108
6^x×3=108
6^x=36
6^x=6^2
x=2
3^x+1×5^x=675
3^x×3×5^x=675
(3×5)^x×3=675
15^x×3=675
15^x=225
15^x=15^2
x=2
3^x+2×7^x-3^x×7^x+1=2940
[tex](3 {}^{2} - 7) \times 3 {}^{x} \times 7 {}^{x} = 2940[/tex]
[tex]2 \times 3 {}^{x} \times 7 {}^{x} = 2940[/tex]
[tex]2 \times 21 {}^{x} = 2940[/tex]
[tex]21 {}^{x} = 1470[/tex]
[tex]x = log_{21}(1470)[/tex]
[tex]x = log_{21}(21 \times 70) [/tex]
[tex]x = log_{21}(21) + log_{21}(70) [/tex]
[tex]x = 1 + log_{21}(70) [/tex]
