CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Property 1

Solve log 2...

Question

Solve ${log}_{2} (3 x - 1) - {log}_{2} (x - 2) = 3$

Open in App

Solution

${log}_{2} (3 x - 1) - {log}_{2} (x - 2) = 3$
${log}_{2} (\frac{3 x - 1}{x - 2}) = 3$ $[∵ {log}_{a} (\frac{M}{N}) = {log}_{a} M - {log}_{a} N]$
$2^{3} = \frac{3 x - 1}{x - 2}$ (exponential form)
$8 = \frac{3 x - 1}{x - 2}$
Cross multiplying, we get
$8 (x - 2) = 3 x - 1 ⟹ 8 x - 16 = 3 x - 1$
$8 x - 3 x = - 1 + 16 ⟹ 5 x = 15$
$∴ x = 3$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Solve the equation

{log}_{2} (3 - x) - {log}_{2} (\frac{s i n \frac{3 π}{4}}{5 - x}) = \frac{1}{2} + {log}_{2} (x + 7)

2 {log}_{2} ({log}_{2} x) + {log}_{\frac{1}{2}} ({log}_{2} 2 \sqrt{2} x) = 1

{log}_{2} [{log}_{3} ({log}_{2} x)] = 1

x

log 2 + log (x + 3) - log (3 x - 5) = log 3

{log}_{1 / 2} (x + 1) > {log}_{2} (2 - x)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Property 1

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon