How do you solve #log_x 16 = 4#?

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Answer 1 · 2018-06-08T06:47:14

#x=2#

#log_2 16=4 " "hArr" "2^4 =16#

Log form and index form are interchangeable.

#log_ab = c " "hArr" " a^c =b#

#log_x 16=4# can be read as asking the question....

"What number, when raised to #4th# power will give #16?#"

In index form this means: #x^4 =16#

It really does help to know the first few powers of the numbers up to #10# by heart.

The powers of #2# are :

#1," "2," "4," "8," "color(blue)(16)," "32," "64," "128 ....#

This means #2^4 =16#, which gives us the answer we need.

#x=2#

Answer 2 · 2018-06-08T06:48:28

#x = 2#

lets say that to put this into exponential form, we can make 4 = y and 16 = the answer.

#x^4 = 16#

#x = 2#