Find x,if log=3/4log16+1/2log25-1/3log8
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Value of x is 20
Step-by-step explanation:
Given,
logx = (3/4) log16 + (1/2) log25 - (1/3) log8
= (3/4) log(2⁴) + (1/2) log(5²) - (1/3) log(2³)
= (3/4 * 4) log2 + (1/2 *2) log5 - (1/3 * 3) log2
= 3 log2 + log5 - log2
= 2 log2 + log5
= log(2²) + log5
= log4 + log5
= log(4 * 5)
= log20
We have, logx = log20
Comparing from both sides, we get
x = 20
Rules:
• log(ab) = loga + logb
• log(a/b) = loga - logb
• log(aᵇ) = b loga
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