anonymous
  • anonymous
Can someone help me solve this for x??? Pls see the logarithm question coming below....
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\log_{1/x}1/z = 1/y \]
anonymous
  • anonymous
more precisely 1 1 log ---- = ----- 1/x z y I have to solve this for x... pls help...
anonymous
  • anonymous
\[\frac{1}{z}=\frac{1}{x}^{\frac{1}{y}}\]Now take each side to exponent y:\[\frac{1}{z}^y=\frac{1}{x}\]Thus,\[x=z^y\]

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anonymous
  • anonymous
Thanks for yr reply but I am unable to understand the reply... Can u pls give a detailed reply......
anonymous
  • anonymous
The first step uses the following property of logs/exponentials. If we have\[\log_{a} c=b\]then,\[c=a^b\]Analogously,\[\log_{\frac{1}{x}} \frac{1}{z}=\frac{1}{y}\]can be re-written,\[\frac{1}{z}=(\frac{1}{x})^{\frac{1}{y}}\]Now we want to get rid of the 1/y exponent. If we take both the left and the right sides of the equality to the power y:\[(\frac{1}{z})^y=((\frac{1}{x}^{\frac{1}{y}})^y)\]Now, this gives us:\[\frac{1^y}{z^y}=(\frac{1}{x})^{\frac{1}{y}*y}\]so,\[\frac{1}{z^y}=(\frac{1}{x})^1\]so,\[x=z^y\]

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