Solve for x, logx 155=2−logx 3515\sqrt{5} = 2 - \text{log}_x \space 3\sqrt{5}155=2−logx 35
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Given,
⇒logx 155=2−logx 35⇒logx 155+logx 35=2⇒logx (155×35)=2⇒logx 225=2⇒x2=225⇒x=225=15.\Rightarrow \text{log}x \space 15\sqrt{5} = 2 - \text{log}x \space 3\sqrt{5} \\[1em] \Rightarrow \text{log}x \space 15\sqrt{5} + \text{log}x \space 3\sqrt{5} = 2 \\[1em] \Rightarrow \text{log}x \space (15\sqrt{5} \times 3\sqrt{5}) = 2 \\[1em] \Rightarrow \text{log}x \space 225 = 2 \\[1em] \Rightarrow x^2 = 225 \\[1em] \Rightarrow x = \sqrt{225} = 15.⇒logx 155=2−logx 35⇒logx 155+logx 35=2⇒logx (155×35)=2⇒logx 225=2⇒x2=225⇒x=225=15.
Hence, x = 15.
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If a2 = log x, b3 = log y and a22−b33\dfrac{a^2}{2} - \dfrac{b^3}{3}2a2−3b3 = log c, find c in terms of x and y.
Given x = log10 12, y = log4 2 × log10 9 and z = log10 0.4, find :
(i) x - y - z
(ii) 13x - y - z
Evaluate :
logb a × logc b × loga c
log3 8 ÷ log9 16
