If 5^(3x)=8, find 5^(3+x)?

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Answer 1 · 2017-06-08T09:59:23

#5^(3 + frac(ln(8))(3 ln(3)))#

We have: #5^(3 x) = 8#

Let's apply #ln# to both sides of the equation:

#Rightarrow ln(5^(3 x)) = ln(8)#

Using the laws of logarithms:

#Rightarrow 3x ln(5) = ln(8)#

#Rightarrow 3 x = frac(ln(8))(ln(3))#

#therefore x = frac(ln(8))(3 ln(3))#

Now, let's evaluate #5^(3 + x)#:

#Rightarrow 5^(3 + x) = 5^(3) cdot 5^(x)#

#therefore 5^(3 + x) = 5^(3 + frac(ln(8))(3 ln(3)))#