Condense the logarithm 4 log_3⁡ a+5 log_3⁡ b - log_3⁡(2x-3)

Question

Please show work/ calculation that's necessary

Answer 1

4·log₃(a) + 5·log₃(b) - log₃(2x-3)

Use the log property b·log(a) = log(a^b):

log₃(a⁴) + log₃(b⁵) - log₃(2x-3)

Use the log property log(a) + log(b) = log(ab):

log₃(a⁴b⁵) - log₃(2x-3)

Use the log property log(a) - log(b) = log(a/b):

log₃(a⁴b⁵/(2x-3))