write log 81 +log64+log5-log72 in the form of log n
Answers
Formulae:
log a + log b = log a×b
log a - log b = log a/b
log a^n = n log a
Soln.
log 81 + log 64 + log 5 - log 72
= log 9² + log 8² + log 5 - log 72
= 2 log 9 + 2 log 8 + log 5 - log 72
= 2 ( log 9 + log 8 ) + log 5 - log 72
= 2 ( log 9×8 ) + log 5 - log 72
= 2 log 72 + log 5 - log 72
= log 72 + log 5
= log 72×5
= log 360
Answer:
The value of the expression
log81+log64+log5-log72 = log360
Step-by-step explanation:
Logarithms:
- Logarithm is the exponent or power to which a base must be raised to obtain a value.
- Mathematically it can be expressed as
- x is logarithm of n to the base a
- if aˣ = n then x = logₐn
- For example if we write 2³ = 8 then we can epress it in logarithms as 3 = log₃8
Some of the formulas used here:
- loga+logb = log(ab)
- loga-logb = log(a/b)
- xᵃ.xᵇ = xᵃ+ᵇ
Given expression is
log81+log64+log5-log72 = log(3)⁴+log(2)⁶+log5-log(2³×3²)
= log(3⁴×2⁶×5)-log(2³×3²)
= log[(3⁴×2⁶×5)/(2³×3²)]
= log[3⁴×2⁶×5×2⁻³×3⁻²]
= log[(3⁴×3⁻²)×(2⁶×2⁻³)×5]
= log[(3⁴⁻²)×(2⁶⁻³)×5]
= log[3²×2³×5]
= log[9×8×5]
= log 360
Hence the value of the expression
log81+log64+log5-log72 = log360
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