Question 22298
<pre><font size = 4><b>You need these facts:

(1)   log<sub>B</sub>A + log<sub>B</sub>C = log<sub>B</sub>(AC)

(2)   If log<sub>B</sub>A = log<sub>B</sub>C then A = C, if B > 0 and B <font face="symbol">¹</font> 1

log<sub>3</sub>5 = log<sub>3</sub>x &#8722; log<sub>3</sub>4

Add log<sub>3</sub>4 to both sides to get as many terms positive as possible

log<sub>3</sub>5 + log<sub>3</sub>4 = log<sub>3</sub>x

Use (1)

log<sub>3</sub>(5·4) = log<sub>3</sub>x

Rewrite 5·4 as 20

log<sub>3</sub>20 = log<sub>3</sub>x  

Use (2):

20 = x

Edwin
AnlytcPhil@aol.com</pre>