The value of 1-log 2 30-1-log 3 30-1-log 5 30 is

The correct option is B 1 1/log_2 30+1/log_3 30+1/log_5 30 =log_30 2+log_30 3+log_30 5 [∵1/log_b a=log_a b] =log_30 (2×3×5) [∵ log_b m+log_b n=log ...

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Byju's Answer

Standard IX

Mathematics

Representation of Logarithmic Function

The value of ...

Question

The value of $\frac{1}{l o g_{2} 30} + \frac{1}{l o g_{3} 30} + \frac{1}{l o g_{5} 30}$ is

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Solution

The correct option is B
1

$\frac{1}{l o g_{2} 30} + \frac{1}{l o g_{3} 30} + \frac{1}{l o g_{5} 30}$

$= l o g_{30} 2 + {log}_{30} 3 + l o g_{30} 5$ [ $∵ \frac{1}{l o g_{b} a} = l o g_{a} b$ ]

$= l o g_{30} (2 \times 3 \times 5)$ [ $∵ l o g_{b} m + l o g_{b} n = l o g_{b} m . n$ ]

$= l o g_{30} 30$

$= 1$

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The value of 1log2 30+1log3 30+1log5 30 is

The correct option is B 1 1log2 30+1log3 30+1log5 30 =log30 2+log30 3+log30 5 [∵1logb a=loga b] =log30 (2×3×5) [∵logb m+logb n=logb m.n] =log30 30 =1

The value of $\frac{1}{l o g_{2} 30} + \frac{1}{l o g_{3} 30} + \frac{1}{l o g_{5} 30}$ is