### Show that X = 2 in the expression below 4^* + 3^* = 5^* Pls...

Show that X = 2 in the expression below
4^* + 3^* = 5^*
Pls note that * is X?

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4* + 3* = 5*
taking log of both sides
logx + logx = logx
4 3 5
making a change of base (all log carrier base 10)
logx + logx = logx
___ ___ ___
log4 log3 log5
log(x-4) + log(x-3) =log(x-5)
log(x-4+x-3) = log(x-4)
2x-7=x-5
2x-x=7-5
x=2
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• Pitch Pee: the question is 4^* + 3^* = 5^*
show that * = 2
the change of base rule wasn't properly applied
5 months ago
4^x + 3^x= 5^x
From Pythagorean triple principle,
the square of a number plus the square of another number should give a corresponding square of a new number.

So,
a^2 + b^2= c^2 is an illustration

Thus, relating the expression, 4^x + 3^x= 5^x to a^2 + b^2= c^2, x should automatically equals 2.

Thank you.
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7^x = 5^x
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Why not just write
4^x + 3^x = 5^x
Hint: Perhaps you should check out the Pythagorean Theorem.
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4^x + 3^x = 5^x
7^x = 5^x
no where to go again
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• Abdulazeez Suleiman: 4*+3*=5*
taking log of both side
logx + logx = logx
4 3 5
making a change of base (all log carries base 10)

logx + logx = logx
___ ___ ___
log4 log3 log5
log(x-4) + log(x-3) = log(x-5)
log(x-4+x-3) = log(x-5)
2x-7=x-5
2x-x=7-5
x=2
5 months ago