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

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 x = log 0.6; y = log 1.25 and z = log 3 - 2 log 2, find the values of :
(i) x+y- z
(ii) 5^{x + y - z}

If a² = log x, b³ = log y and 3a² - 2b³ = 6 log z, express y in terms of x and z .

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

Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.

If a² = log x , b³ = log y and `a^2/2 - b^3/3` = log c , find c in terms of x and y.

Given x = log₁₀12 , y = log₄ 2 x log₁₀9 and z = log₁₀0.4 , find :
(i) x - y - z
(ii) 13^{x - y - z}

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

State, true of false:

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

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

Express the following in a form free from logarithm:
`2"log" x + 1/2"log" y` = 1