How do you solve #log_9(x^7)=15 #?

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Answer 1 · 2015-12-16T23:49:50

#x = 9^(15/7)#

From the definition of a logarithm, we have

#a^(log_a(x)) = x#

Applying that here, we get

#log_9(x^7) = 15#

#=> 9^(log_9(x^7)) = 9^15#

#=> x^7 = 9^15#

#=> x = (9^15)^(1/7) = 9^(15/7)#

Answer 2 · 2015-12-17T04:05:04

#x=9^(15/7)#

Use the logarithm rule: #log_a(b^c)=c*log_a(b)#

Thus, the equation can be rewritten as

#7log_9(x)=15#

Divide both sides by #7#

#log_9(x)=15/7#

Undo the logarithm

#9^(log_9(x)=9^(15/7)#

#x=9^(15/7)#