How do you solve $log x = 5 log 4$ $Log x = 5 Log 4$ ?

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How do you solve $log x = 5 log 4$ $Log x = 5 Log 4$ ?

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Answer 1 · 2016-03-19T04:15:01

$x = 1024$ $x=1024$

Explanation:

$1$ $1$ . Use the log property, ${log}_{b} m^{n} = n \cdot {log}_{b} m$ $log_color(purple)bcolor(red)m^color(blue)n=color(blue)n*log_color(purple)bcolor(red)m$ , to rewrite $5 log 4$ $5log4$ .

$log x = 5 log 4$ $logx=5log4$

$log x = {log 4}^{5}$ $logx=log4^5$

$2$ $2$ . Since the equation now follows a " $log = log$ $log=log$ " situation, where the bases are the same on both sides, rewrite the equation without the "log" portion.

$x = 4^{5}$ $x=4^5$

$3$ $3$ . Solve for $x$ $x$ .

$color(green)(|bar(ul(color(white)(a/a)x=1024color(white)(a/a)|)))$

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How do you solve $log x = 5 log 4$ $Log x = 5 Log 4$ ?

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How do you solve $log x = 5 log 4$ $Log x = 5 Log 4$ ?