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stealth61 [152]
4 years ago
5

If f(x)=log10x, what is the approximate value of y in the equation 10^y=5?

Mathematics
1 answer:
Simora [160]4 years ago
7 0
\bf log_{{  a}}\left( x^{{  b}} \right)\implies {{  b}}\cdot  log_{{  a}}(x)\\\\
-----------------------------\\\\
10^y=5\implies log(10^y)=log(5)\implies ylog(10)=log(5)\\\\\\ y=\cfrac{log(5)}{log(10)}\\\\
-----------------------------\\\\
\textit{Logarithm Change of Base Rule}\\\\
log_{{  a}}{{  b}}\implies \cfrac{log_{{  c}}{{  b}}}{log_{{  c}}{{  a}}}\\\\
-----------------------------\\\\
y=\cfrac{log(5)}{log(10)}\iff y = log_{10}(5)\iff y=log(5)
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