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# Exponents

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99
2

What is the value of b if 5^b + 5^b + 5^b + 5^b + 5^b = 25^(b - 1).

Jul 14, 2021

#1
+3

Answer: $$3$$

Solution:

$$5^b\cdot5$$ (essentially what you wrote except using multiplication) can be turned into $$5^{b+1}$$$$25^{b-1}$$ can be turned into $$5^{2(b-1)}$$, or $$5^{2b-2}$$. Now you have to set these two equal to each other:

$$5^{b+1}$$$$5^{2b-2}$$

You can get rid of the base, because they're the same.

$$b+1=2b-2$$

Subtracting $$b$$ from both sides and adding 2 gives $$b=3$$

Jul 14, 2021

#1
+3

Answer: $$3$$

Solution:

$$5^b\cdot5$$ (essentially what you wrote except using multiplication) can be turned into $$5^{b+1}$$$$25^{b-1}$$ can be turned into $$5^{2(b-1)}$$, or $$5^{2b-2}$$. Now you have to set these two equal to each other:

$$5^{b+1}$$$$5^{2b-2}$$

You can get rid of the base, because they're the same.

$$b+1=2b-2$$

Subtracting $$b$$ from both sides and adding 2 gives $$b=3$$

WhyamIdoingthis Jul 14, 2021
#2
+1

Very nice, WhyamIdoingthis....!!!!   CPhill  Jul 14, 2021