How do you solve #5= \log _ { 2} 16^ { x }#?

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Answer 1 · 2017-07-22T00:47:30

#x = 5/4#

This expression can also be rearranged to exponential form:

#5 = log_2(16^x)#

#2^5 = color(red)(16^x#

What we can do here is get each base to be the same, so that we can then solve for the exponents:

Note that the number #color(red)(16# is equal to #color(red)(2^4#, so we can also write the above equation as

#2^5 = color(red)(2^(4x)#

Now that the bases are equal, we can set the exponents equal to each other and solve for #x#:

#5 = 4x#

#x = color(blue)(5/4#