Solve: log 3 x · log 4 x · log 5 x = log 3 x · log 4 x + log 4 x · log 5 x + log 5 x · log 3 x

log 3 x · log 4 x · log 5 x = log 3 x · log 4 x + log 4 x · log 5 x + log 5 x · log 3 x Let, log x 3 = p ⇒ log 3 x = 1 p , log x 4 = q ⇒ log 4 x = 1 q , log x 5 = r ⇒ log 5 x = 1 r From given equation: ⇒ 1 p q r = 1 p q + 1 q r + 1 p r ⇒ 1 p q r = r p q r + p p q r + q p q r ⇒ p + q + r = 1 ⇒ log x 3 + log x 4 + log x 5 = 1 ⇒ log x 60 = 1 ⇒ x = 60

E M B I B E

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 1 - Logarithm and Its Applications>DPP>Q 10

HARD

JEE Main

IMPORTANT

Earn 100

If $\log_{a} b = 2, \log_{b} c = 2$ and $\log_{3} c = 3 + \log_{3} a$ then the value of $\frac{c}{a b}$ is

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Important Questions on Logarithm and Its Applications

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 1 - Logarithm and Its Applications>DPP>Q 11

If

\log_{2} 10 = p, \frac{\log_{e} 10}{\log_{e} 7} = q

and

11^{r} = 10,

then which one of the following expression is equivalent to

\log_{10} 154 ?

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 1 - Logarithm and Its Applications>DPP>Q 12

If

3^{{(\log_{3} 7)}^{x}} = 7^{{(\log_{7} 3)}^{x}}

then the value of

x

will be

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 1 - Logarithm and Its Applications>DPP>Q 13

The value of

4^{5 \log_{4 \sqrt{2}} (3 - \sqrt{6}) - 6 \log_{8} (\sqrt{3} - \sqrt{2})}

is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 1 - Logarithm and Its Applications>DPP>Q 14

The value of:

\frac{81^{\frac{1}{\log_{5} 9}} + 3^{\frac{3}{\log_{\sqrt{6}} 3}}}{409} ({(\sqrt{7})}^{\frac{2}{\log_{25} 7}} - {((125))}^{\log_{25} 6})

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 1 - Logarithm and Its Applications>DPP>Q 15

The value of

6^{\log_{10} 40} \cdot 5^{\log_{10} 36}

is:

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 1 - Logarithm and Its Applications>DPP>Q 1

Find the value of

x

satisfying the equations

\log_{3} (\log_{2} x) + \log_{1 / 3} (\log_{1 / 2} y) = 1

and

x y^{2} = 9

.

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 1 - Logarithm and Its Applications>DPP>Q 2

Let $a$ and $b$ be real numbers greater than $1$ for which there exists a positive real number $c,$ different from $1,$ such that $2 (\log_{a} c + \log_{b} c) = 9 \log_{a b} c .$ Find the largest possible value of $\log_{a} b .$