How do you solve $log x - log (9x+4)= -1$ ?

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Answer 1 · 2016-02-27T03:45:24

Use the rule $log_an - log_am = log_a(n/m)$ to simplify

$log((x)/(9x + 4)) = -1$

Convert to exponential form. The log is in base 10, since nothing is noted in subscript beside the log.

$x/(9x + 4) = 10^-1$

$x/(9x + 4) = 1/10^1$

$x/(9x + 4) = 1/10$

Simplify using the rule $a/b = m/n -> a xx n = b xx m$

$x(10) = (9x + 4)1$

$10x = 9x + 4$

$10x - 9x = 4$

$x = 4$

How do you solve log x - log (9x+4)= -1log x - log (9x+4)= -1?