How do you solve #5^(x+3)=6#?

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Answer 1 · 2015-11-26T07:50:01

#x = ln(6)/ln(5) - 3#

We will use the property that
#ln(a^x) = xln(a)#

#5^(x+3) = 6#

#=> ln(5^(x+3)) = ln(6)#

#=>(x+3)ln(5) = ln(6)# #" "#(by the above property)

#=> x + 3 = ln(6)/ln(5)#

#=> x = ln(6)/ln(5) - 3#

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Note that we can easily check the answer by using the property #ln(a)/ln(b) = log_b(a)#

Then
#5^(ln(6)/(ln(5))+3 - 3) = 5^(ln(6)/ln(5)) = 5^(log_5(6)) = 6#