Question #252ab

1 Answer
Nov 5, 2016

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)