SOLUTION: solve each equation by first rewriting the expression in each part with the same base c. 4^2x=(1/2)^x+5

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Question 1076076: solve each equation by first rewriting the expression in each part with the same base
c. 4^2x=(1/2)^x+5
Found 3 solutions by MathLover1, jorel1380, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

c.
4%5E%282x%29=%281%2F2%29%5E%28x%2B5%29
4%5E%282x%29=1%5E%28x%2B5%29%2F2%5E%28x%2B5%29........since 1%5E%28x%2B5%29 always will be equal 1, we have
%282%5E2%29%5E%282x%29=1%2F2%5E%28x%2B5%29
2%5E%284x%29=2%5E%28-%28x%2B5%29%29
2%5E%284x%29=2%5E%28-x-5%29
4x=-x-5
4x%2Bx=-5
5x=-5
x=-5%2F5
x=-1

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
4^2x=(1/2)^(x+5)
4^2x=((4^-0.5)^(x+5)
4^2x=4^(-0.5x-2.5)
2x=(-x-5)/2
4x=-x-5
5x=-5
x=-1
☺☺☺☺

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve each equation by first rewriting the expression in each part with the same base
c. 4^2x=(1/2)^x+5
matrix%281%2C3%2C+4%5E%282x%29%2C+%22=%22%2C+%281%2F2%29%5E%28x+%2B+5%29%29

matrix%281%2C3%2C+2%5E%284x%29%2C+%22=%22%2C+%282%5E%28-+1%29%29%5E%28x+%2B+5%29%29 ------ Converting  and matrix%281%2C3%2C+1%2F2%2C+to%2C+2%5E%28-+1%29%29

matrix%281%2C3%2C+2%5E%284x%29%2C+%22=%22%2C+2%5E%28-+1%28x+%2B+5%29%29%29

4x = - 1(x + 5) ------- Bases are equal and so are the exponents

4x = - x - 5

4x + x = - 5

5x = - 5

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+%28-+5%29%2F5%2C+or%2C+-+1%29%29