Question

Can someone help me solve this for x??? Pls see the logarithm question coming below....

Answer 1

\[\log_{1/x}1/z = 1/y \]

Answer 2

more precisely
1 1
log ---- = -----
1/x z y

I have to solve this for x...
pls help...

Answer 3

\[\frac{1}{z}=\frac{1}{x}^{\frac{1}{y}}\]Now take each side to exponent y:\[\frac{1}{z}^y=\frac{1}{x}\]Thus,\[x=z^y\]

Answer 4

Thanks for yr reply but I am unable to understand the reply...
Can u pls give a detailed reply......

Answer 5

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,\[x=z^y\]