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305
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avatar+2653 

Please don't give me the answer 

 

But give me an idea how to solve it

 

\(5^{x+1}=30\), then what is \(5^{3x+1}\)

 

I had a bogus solution of 1080 that is probably wrong

 Mar 28, 2019
 #1
avatar+28471 
+2

5x+1 can be written as 5x*5, so if this equals 30, you can find what 5x equals.

 

53x+1 can be written as 53x*5, which can be written as (5x)3*5, so once you know what 5x is you just cube it and multiply by 5.

 Mar 28, 2019
 #2
avatar+2653 
+3

Ok, thank you! My answer of 1080 is right and I understand.

 Mar 28, 2019
 #3
avatar+20217 
0

You could also use the log function if you are familiar with that:

 

5x+1 =30

 

log(5x+1)=log30

x+1 = log30/log5

x+1 = 2.113282752559378-1 = 1.113282752559378

 

Then  53x+1 = 5^4.339848257678134 = 1079.999999999998196774=~~1080

 Mar 28, 2019
 #4
avatar+4330 
0

Yex, \(5^{x+1}=5^x*5^1=30 \longrightarrow 5^x=6.\) Breaking. \(5^{3x+1}=5^{3x}*5^1, (5^x)^3*5^1=(6)^3*5=\boxed{1080}.\)

.
 Mar 28, 2019

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