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If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?

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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
since the values are equal
the powers can be equated.
we therefore have

4x=9-x
x=3
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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?

A. 5
B. 4
C. 3
D. 2
E. 1

Since the bases of both sides are -5 and 5, the exponents of both sides should be even numbers(i. e. 4x and 9+x should be even numbers).

Moreover they should be equal since the absolute values of the bases are equal.
That is 4x=9+x ---> x=3. The answer is, therefore, C.
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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Since (-5)^4x = 5^(9+x)

Thus both sides are equal: Hence x>0

4x = 9+x
x = 3

Ans: 3
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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
(-5)^4x = 5^(9+x)

Negative on LHS is not needed as any multiple of 4 will be an even integer, canceling out the negative, thus we can drop it and treat it as 5. Since both sides will now have 5 as a common base, we can equate the exponents and solve.

4x=9+x
3x=9
x=3
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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Bunuel wrote:
If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?

A. 5
B. 4
C. 3
D. 2
E. 1

(-5)^(4x) = 5^(9 + x) = -1(4x)*(5)^(4x) = 5^(9 + x)

Or, 4x = 9 + x

Or, 3x = 9

Or, x = 3

Hence answer will be (C) 3
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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
simple and good question
First few seconds I tried solving as$$\frac{1}{5^{4x}}$$
Later, I substituted options
Any negative value raised to an Even power is always become Positive value
Thanks for explanations
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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Bunuel wrote:
If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?

A. 5
B. 4
C. 3
D. 2
E. 1

Since x is an integer, 4x is even, and (-5)^(4x) = 5^(4x). Thus, we can drop the bases, equate the exponents, and solve for x.

4x = 9 + x

3x = 9

x = 3

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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
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