Question

simplify log 216+[log 42- log 6 / log 49]​

Answer 1

hey mate remember formula

log(ab)=loga+logb

log(a/b)=loga-logb

loga*2=2loga

loge=1

now

log216+(log42-log6/log49)

log216+(log42/6/log49

log 216+(log7/log49)

log216+(log7/log7*2)

log 216+(log7/2log7)

log 216+1/2

2log216+loge/2

log216*2e/2

Answer 2

The value of given expression is 2.834.

Step-by-step explanation:

The given expression is

$\log 216+[\dfrac{\log42-\log6}{\log 49}]$

Using the properties of logarithm we get

$\log (8\times 27)+[\dfrac{\log(\frac{42}{6})}{\log 49}]$       $[\because \log(\frac{a}{b})=\log a-\log b]$

$\log (2^3\cdot 3^3)+[\dfrac{\log 7}{\log (7)^2}]$

$\log (2^3)\cdot \log (3^3)+[\dfrac{\log 7}{\log (7)^2}]$     $[\because \log(ab)=\log a+\log b]$

$3\log 2+3\log 3+[\dfrac{\log 7}{2\log (7)}]$       $[\because \log a^b=b\log a]$

$3(0.301)+3(0.477)+\dfrac{1}{2}$

$2.834$

Therefore, the value of given expression is 2.834.

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Simplification using Properties of logarithm:

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