How do you solve #(3/4)^x=27/64#?

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Answer 1 · 2018-07-03T14:00:20

#color(blue)(x=3)#

We could solve this by the use of logarithms in the following way:

Taking logs of both sides. It dosen't matter which base you use as long as you use the same on both sides.

#xln(3/4)=ln(27/64)#

#x=(ln(27/64))/(ln(3/4))=3#

This method requires the use of a calculator or tables. We can solve this without these:

Notice we can write:

#27=3^3#

#64=4^3#

#:.#

#(3/4)^x=(3^3)/(4^3)#

By the laws of indices:

#(3^3)/(4^3)=(3/4)^3#

#:.#

#(3/4)^x=(3/4)^3#

Since both bases are the same, both exponents are equal:

#:.#

#x=3#