Solve the Following: Log 7 + Log (3x - 2) = Log (X + 3) + 1 - Mathematics

Solve the following:
log 7 + log (3x - 2) = log (x + 3) + 1

Sum

log 7 + log (3x - 2) = log (x + 3) + 1
⇒ log 7 + log (3x - 2) - log (x + 3) = 1
⇒ `"log"(7.(3x - 2))/(x + 3)` = log 10

⇒ `(7.(3x - 2))/(x + 3)` = 10
⇒ 21x - 14 = 10(x + 3)
⇒ 21x - 10x = 30 + 14
⇒ 11x = 44
⇒ x = 44 / 11 = 4.

shaalaa.com

More About Logarithm

Is there an error in this question or solution?

Chapter 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 7.3

If m = log 20 and n = log 25, find the value of x, so that :
2 log (x - 4) = 2 m - n.

Given log₁₀x = 2a and log₁₀y = `b/2`. Write 10^{2b + 1} in terms of y.

Evaluate: log_ba × log_c b × log_a c.

Solve : log₅( x + 1 ) - 1 = 1 + log₅( x - 1 ).

Evaluate: `(log_5 8)/(log_25 16 xx Log_100 10)`

Solve the following:
log ₄ x + log₄(x-6) = 2

State, true of false:

If `("log"49)/("log"7)` = log y, then y = 100.

If 2 log x + 1 = log 360, find: log(2 x -2)

Express the following in a form free from logarithm:
3 log x - 2 log y = 2

If a = log 20 b = log 25 and 2 log (p - 4) = 2a - b, find the value of 'p'.