How do you solve #3^(5x)*81^(1-x)=9^(x-3)#?

Answer 1

Add a shared base.

#3^(5x) xx (3^4)^(1 - x) = (3^2)^(x - 3)#
Simplify using the rules #a^n xx a^m = a^(n + m)# and #(a^n)^m = a^(n xx m)#.
#3^(5x) xx 3^(4 - 4x) = 3^(2x - 6)#
#3^(5x + 4 - 4x) = 3^(2x - 6)#

Now that the bases have been removed, we can solve like a linear equation.

#5x + 4 - 4x = 2x - 6#
#5x - 4x - 2x = -6 - 4#
#-x = -10#
#x = 10#

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Answer 2

#x = 10#

#3^(5x)*81^(1-x) = 9^(x-3)#
#=> 3^(5x)*(3^4)^(1 - x) = (3^2)^(x-3)#
#=> 3^(5x)*3^(4(1-x)) = 3^(2(x-3))#
#=>3^(5x + 4 - 4x) = 3^(2x - 6)#
#=> 3^(x + 4) = 3^(2x - 6)#
Apply #log_3# to both sides
#=> log_3 3^(x + 4) = log_3 3^(2x - 6)#
#=> (x + 4) log_3 3 = (2x - 6)log_3 3#
#=> x + 4 = 2x - 6#
#=> x = 10#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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