# Find the value of t for the given expression.

${{\log }_{2}}\left[ {{\log }_{3}}\left( \log 2t \right) \right]=1$

A. 512

B. 128

C. 1024

D. None

Answer

Verified

361.5k+ views

Hint: Use logarithm properties and formulas to simplify the equation.Start by opening the outermost log by the formula ${{\log }_{a}}b=x,b={{a}^{x}}$ to find the value of t.

“Complete step-by-step answer:”

${{\log }_{2}}\left[ {{\log }_{3}}\left( \log 2t \right) \right]=1$

Base of the above logarithm is 2.

We write the above log in exponential form.

$\left[ When\ {{\log }_{a}}b=x,b={{a}^{x}} \right]$

Therefore, ${{\log }_{3}}\left( {{\log }_{2}}t \right)={{2}^{1}}$

$\Rightarrow {{\log }_{3}}\left( {{\log }_{2}}t \right)=2$

Base of the above logarithm is 3.

We again write it in exponential form.

Therefore, ${{\log }_{2}}t={{3}^{2}}$

$\Rightarrow {{\log }_{2}}t=9$

The base of the above logarithm is 2.

We write it in exponential form.

Therefore, $t={{2}^{9}}$

$\Rightarrow t=512$

Note: While solving the above question, do the calculation carefully.

Start by opening the outermost log and apply the logarithmic properties and formulas wherever necessary.

“Complete step-by-step answer:”

${{\log }_{2}}\left[ {{\log }_{3}}\left( \log 2t \right) \right]=1$

Base of the above logarithm is 2.

We write the above log in exponential form.

$\left[ When\ {{\log }_{a}}b=x,b={{a}^{x}} \right]$

Therefore, ${{\log }_{3}}\left( {{\log }_{2}}t \right)={{2}^{1}}$

$\Rightarrow {{\log }_{3}}\left( {{\log }_{2}}t \right)=2$

Base of the above logarithm is 3.

We again write it in exponential form.

Therefore, ${{\log }_{2}}t={{3}^{2}}$

$\Rightarrow {{\log }_{2}}t=9$

The base of the above logarithm is 2.

We write it in exponential form.

Therefore, $t={{2}^{9}}$

$\Rightarrow t=512$

Note: While solving the above question, do the calculation carefully.

Start by opening the outermost log and apply the logarithmic properties and formulas wherever necessary.

Last updated date: 27th Sep 2023

•

Total views: 361.5k

•

Views today: 9.61k

Recently Updated Pages

What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Why are resources distributed unequally over the e class 7 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE

What is the past tense of read class 10 english CBSE