Prove the divisibility of the following numbers: a)7^6+7^5−7^4 by 11 b)5^5−5^4+5^3 by 7 c)51^7−51^6 by 25 d)25^7+5^13 by

2 answers
Question:

Prove the divisibility of the following numbers:
a)7^6+7^5−7^4 by 11
b)5^5−5^4+5^3 by 7
c)51^7−51^6 by 25
d)25^7+5^13 by 30
e)16^5+2^15 by 33
PLS HELP NEEDED AS SOON AS POSSIBLE
20 points will be rewarded
correct answers on all of them will be marked as brainliest answer
THX

Answers

[tex]x=2[/tex]

Step-by-step explanation:

So we have the equation:

[tex]5^x+5^{x+1}=150[/tex]

First, separate the second term:

[tex]5^x+(5\cdot5^x)=150[/tex]

Let u equal 5ˣ. So:

[tex]u+5u=150[/tex]

Combine like terms:

[tex]6u=150[/tex]

Divide both sides by 6:

[tex]u=25[/tex]

Substitute back u:

[tex]5^x=25[/tex]

Take the base 5 logarithm of both sides:

[tex]\log_5(5^x)=\log_5(25)[/tex]

The left cancels:

[tex]x=\log_5(25)[/tex]

Evaluate the right:

[tex]x=2[/tex]

So, our answer is 2.

And we're done!

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