Solve the following equation:
log(10x + 5) - log(x - 4) = 2
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Given,
⇒log(10x+5)−log(x−4)=2log 10⇒log10x+5x−4=log 102⇒10x+5x−4=100⇒10x+5=100(x−4)⇒10x+5=100x−400⇒100x−10x=405⇒90x=405⇒x=40590⇒x=4.5\Rightarrow \text{log}(10x + 5) - \text{log}(x - 4) = 2\text{log } 10 \\[1em] \Rightarrow \text{log}\dfrac{10x + 5}{x - 4} = \text{log } 10^2 \\[1em] \Rightarrow \dfrac{10x + 5}{x - 4} = 100 \\[1em] \Rightarrow 10x + 5 = 100(x - 4) \\[1em] \Rightarrow 10x + 5 = 100x - 400 \\[1em] \Rightarrow 100x - 10x = 405 \\[1em] \Rightarrow 90x = 405 \\[1em] \Rightarrow x = \dfrac{405}{90} \\[1em] \Rightarrow x = 4.5⇒log(10x+5)−log(x−4)=2log 10⇒logx−410x+5=log 102⇒x−410x+5=100⇒10x+5=100(x−4)⇒10x+5=100x−400⇒100x−10x=405⇒90x=405⇒x=90405⇒x=4.5
Hence, x = 4.5
Answered By
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log(2x + 3) = log 7
log(x + 1) + log(x - 1) = log 24
log105 + log10(5x + 1) = log10(x + 5) + 1
log(4y - 3) = log(2y + 1) - log 3
