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devi321
@devi321
October 2021
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Помогите срочно!!! Математика, решить подробно, ответ без log
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nKrynka
Решение
3^(x + 4) - 5^(x + 3) = 3*x - 5^(x + 2)
(3^x)*(3⁴) - (5^x)*(5³) = 3^x - (5^x)*(5²)
(3^x)*(3⁴) - 3^x = (5^x)*(5³) - (5^x)*(5²)
(3^x)*(3⁴ - 1) = (5^x)*(5³ - 5²)
(3^x)*80 = (5^x)*100
(3/5)^x = 100/80
(3/5)^x = 10/8
(3/5)^x = 5/4
log₃/₅ [(3/5)^x] = log₃/₅ (5/4)
x = log₃/₅ (5/4)
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Answers & Comments
3^(x + 4) - 5^(x + 3) = 3*x - 5^(x + 2)
(3^x)*(3⁴) - (5^x)*(5³) = 3^x - (5^x)*(5²)
(3^x)*(3⁴) - 3^x = (5^x)*(5³) - (5^x)*(5²)
(3^x)*(3⁴ - 1) = (5^x)*(5³ - 5²)
(3^x)*80 = (5^x)*100
(3/5)^x = 100/80
(3/5)^x = 10/8
(3/5)^x = 5/4
log₃/₅ [(3/5)^x] = log₃/₅ (5/4)
x = log₃/₅ (5/4)