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What is the expression for f(x), when we rewrite \(3^{5x+3} \cdot 27^{x}\), as \(3^{f(x)}\) ?

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:equivalent-exp/e/rewrite-exponential-expressions

 

I need help with this problem, and I watched the video before it but it was confusing for me. Could somebody explain the question or help me solve it?

Thank you,

\(tommarvoloriddle\)

 

 

 

EDIT:

 

Ok, I forgot to include what I tried and what I am stuck on:

\(3^{3^{5x+3} \cdot 27^{x}}\)

Then I simplified a bit:

\(\)\(3^{3^{8x+3}}\)

and now, I have no idea what to do.

It would be great if you could help from there!

 Aug 10, 2019
edited by tommarvoloriddle  Aug 10, 2019
edited by tommarvoloriddle  Aug 10, 2019
edited by tommarvoloriddle  Aug 10, 2019
 #1
avatar+103122 
+2

3^(5x + 3) *  27^x

 

Note that 27^x  = (3^3)^x     =  3^(3x)   ....so we have....

 

3^(5x + 3) * 3^(3x)        using a property of exponents   we can write

 

3^( 5x + 3  + 3x)  =

 

3^( 8x + 3)   

 

So  f(x)   =  8x + 3

 

 

cool cool cool

 Aug 10, 2019
 #2
avatar+1342 
+2

Thank you!

tommarvoloriddle  Aug 11, 2019

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