How do you solve #log_6 (x-4) ^2=2#?

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How do you solve #log_6 (x-4) ^2=2#?

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Answer 1 · 2018-05-09T14:26:57

#x_"1"=4+6^sqrt2#
#x_"2"=4+1/(6^sqrt2)#

Explanation:

#log_"6"(x-4)²=2#
#(ln(x-4)/ln(6))²=2#
#ln(x-4)/ln(6)=±sqrt2#
#ln(x-4)=±ln(6)sqrt2#
#x-4=6^(±sqrt2)#
#x=4+6^(±sqrt2)#
#x_"1"=4+6^sqrt2#
#x_"2"=4+1/(6^sqrt2)#
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How do you solve #log_6 (x-4) ^2=2#?

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