Formula1" title=" \sqrt{2x + 3 } - \sqrt{x - 2} = 2 " alt=" \sqrt{2x + 3 } - \sqrt{x - 2} = 2 " align="absmiddle" class="latex-formula">
find x
find x
1 answer:
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x = 3 or x = 1
note that log 5 is usually taken to mean 5
using the law of logarithms
logx - logy = log ()
the right hand side can be expressed as
log 10000 - log 16 = log () = log 625
divide both sides by log 5
x² - 4x + 7 = = 4
subtract 4 from both sides
x² - 4x + 3 = 0 ← in standard form
(x - 3 )(x - 1) = 0
equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 1 = 0 ⇒ x = 1