log₇ 49 = 2, because 7^2 = 49log₅ 125 = 3, because 5^3 = 125log₃ 81 = 4, because 3^4 = 81log₂ 32 = 5, because 2^5 = 32lg 10000 = 4, because 10^4 = 10000lg 10710^7107 = 7, because 10^7 = 10000000lg 0.001 = -3, because 10^-3 = 0.001lg 0.00001 = -5, because 10^-5 = 0.00001
So the values of the given logarithms are: log₇ 49 = 2 log₅ 125 = 3 log₃ 81 = 4 log₂ 32 = 5 lg 10000 = 4 lg 10710^7107 = 7 lg 0.001 = -3 lg 0.00001 = -5
Let's solve each logarithm:
log₇ 49 = 2, because 7^2 = 49log₅ 125 = 3, because 5^3 = 125log₃ 81 = 4, because 3^4 = 81log₂ 32 = 5, because 2^5 = 32lg 10000 = 4, because 10^4 = 10000lg 10710^7107 = 7, because 10^7 = 10000000lg 0.001 = -3, because 10^-3 = 0.001lg 0.00001 = -5, because 10^-5 = 0.00001So the values of the given logarithms are:
log₇ 49 = 2
log₅ 125 = 3
log₃ 81 = 4
log₂ 32 = 5
lg 10000 = 4
lg 10710^7107 = 7
lg 0.001 = -3
lg 0.00001 = -5