solve change of base exponents: If 10^x=2^y, 5^x=2^z, find z  TOPIC_SOLVED

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solve change of base exponents: If 10^x=2^y, 5^x=2^z, find z

Postby t_line on Thu Apr 30, 2009 4:55 pm

Without a calculator, how do you solve for z?

Given: 10^x = 2^y

Find z if: 5^x = 2^z

choices: 2^(x+y), 2^(y-x), 2^(y/x), or 2^(y+1)

Clearly z will be less than y, since 5^x is much less than 10^x... but beyond that I cannot go.
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Postby stapel_eliz on Thu Apr 30, 2009 8:06 pm

t_line wrote:Given: 10^x = 2^y

Find z if: 5^x = 2^z

Since 10x = (5*2)x = (5x)(2x), and since 5x = 2z, then 10x = (2z)(2x) = 2z + x.

Since 10x = 2y, then 2z + x = 2y.

Then what does z + x equal? :wink:
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