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Simora [160]
4 years ago
7

What is the following is the solution to the equation 25^(z+2) = 125

Mathematics
1 answer:
maksim [4K]4 years ago
3 0

First, rewrite the equation 25^{z+2} = 125 with the base equal to 5. Note that:

  • 25=5^2;
  • 125=5^3;
  • 25^{z+2}=(5^2)^{z+2}=5^{2\cdot (z+2)}.

Then

5^{2\cdot (z+2)}=5^3.

Since the bases are equal, you have that powers are equal too:

2\cdot (z+2)=3,\\ \\2z+4=3,\\ \\2z=3-4,\\ \\2z=-1,\\ \\z=-\dfrac{1}{2}.

Answer: z=-\dfrac{1}{2}.


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