Question

log3=0.4771 log4=0.6020 find log512 to the base 5​

Answer 1

Answer:

3.8755

Step-by-step explanation:

log3=0.4771 log4=0.6020 find log₅512

logₙm = logₐm / logₐn

so, log₅512 = log 512 / log 5

                  = log 2⁹ / log (10/2)

                  = [9*log2] / [log10-log2]

                  = [9* log4¹/²]  / [ 1 - log4¹/²]

                  = [9/2 * log4] / [ 1- (1/2)*log4]

                  = [9/2 * 0.6020] / [1- (1/2)*0.6020]

                  = [9* 0.3010] / [ 1 - 0.3010 ]

                  = 2.7090 / 0.699

                  = 3.8755