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Property 3

i If log a+1=...

Question

(i) If $l o g (a + 1) = l o g (4 a - 3) - l o g 3$ ; find a.

(ii) If $2 l o g y - l o g x - 3 = 0$ , express x in terms of y.

(iii) Prove that : $l o g_{10} 125 = 3 (1 - l o g_{10} 2)$ .

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Solution

(i)

$g i v e n space t h a t log open parentheses a plus 1 close parentheses equals log open parentheses 4 a minus 3 close parentheses minus log 3 rightwards double arrow log open parentheses a plus 1 close parentheses equals log open parentheses fraction numerator 4 a minus 3 over denominator 3 end fraction close parentheses rightwards double arrow a plus 1 equals fraction numerator 4 a minus 3 over denominator 3 end fraction rightwards double arrow 3 a plus 3 equals 4 a minus 3 rightwards double arrow a equals 6$

(ii)

(iii)

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Similar questions

2 log y - log x - 3 = 0

x

y .

2 log y - log x - 3 = 0

x

y .

log (\frac{x + y}{3}) = \frac{1}{2} log x + \frac{1}{2} log y

then show that,

\frac{x}{y} + \frac{y}{x} = 7

{log}_{b} a^{5} . {log}_{c} b^{3} . {log}_{a} c^{7} = 105

log (a + 1) = log (4 a - 3) - log 3

, then the value of

a

2 log y - log x - 3 = 0

x = \frac{y^{2}}{m}

, then the value of

m

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