Question #252ab

1 Answer
Nov 5, 2016

Answer:

#x = ln(30)/ln(24) = log_24(30)#

Explanation:

#4^x/5 = 6^(1-x)#

Apply the property of exponents that #a^(x+y) = a^x*a^y#

#=>4^x/5 = 6^1*6^(-x)#

Multiply both sides by #5*6^x#. Note that #6^(-x)*6^x = 6^0 = 1#

#=> 4^x*6^x = 30#

Apply the property of exponents that #a^x*b^x = (ab)^x#

#=> (4*6)^x = 30#

#=> 24^x = 30#

Take a logarithm of both sides

#=> ln(24^x) = ln(30)#

Apply the property of logarithms that #ln(a^x) = xln(a)#

#=> xln(24) = ln(30)#

#:. x = ln(30)/ln(24) = log_24(30)#