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Solve for x : log_10 (x+6) - log_10 x=2?

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Solve for x : log_10 (x+6) - log_10 x=2?

asked Apr 20, 2013 in ALGEBRA 2 by linda Scholar
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2 Answers

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italic log subscript 10 open parentheses x plus 6 close parentheses minus italic log subscript 10 open parentheses x close parentheses equal 2

italic log subscript 10 fraction numerator open parentheses x plus 6 close parentheses over denominator x end fraction equal 2                    (Logarithms formula : italic log subscript 10 open parentheses a close parentheses minus italic log subscript 10 open parentheses b close parentheses equal italic log subscript 10 open parentheses a over b close parentheses)

fraction numerator open parentheses x plus 6 close parentheses over denominator x end fraction equal open parentheses 10 to the power of 2 close parentheses                     ( Remove logarithm)

x plus 6 equal 100 x

6 equal 99 x

2 equal 33 x

x equal 2 over 33.

answered Apr 20, 2013 by diane Scholar
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The logarithmic equation is image

Apply the quotient property image

image

Convert the logarithmic term to exponential term with base 10 and exponent 2.

image

image

image

image

image

image

Solution

image

answered Jul 8, 2014 by david Expert

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