LOGARITHMS - 1

If Log_y81 – log₅3125 = -1; find y

Solution

Log_y81 – Log₅5⁵ = -1        3135=5x5x5x5x5=5⁵ by prime factorization

Log_y81 – 5Log₅5 = -1

Log_y81 – 5x1 = -1

Log_y81 – 5 = -1

Log_y81 = -1 + 5

Log_y81 = 4

81 = y⁴                   81=3x3x3x3 = 3⁴ by prime factorization

3⁴ = y⁴

3 =y

Hence y = 3