Solve : log 5 (x + 1) - 1 = 1 + log 5 (x - 1).

Given, ⇒ log 5 (x + 1) - 1 = 1 + log 5 (x - 1) ⇒ log 5 (x + 1) - log 5 (x - 1) = 1 + 1 ⇒ log 5 = 2 ⇒ ⇒ x + 1 = 25(x - 1) ⇒ x + 1 = 25x - 25 ⇒ 25x - x = 1 + 25 ⇒ 24x = 26 ⇒ x = . Hence, x = .

Mathematics

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

Logarithms

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Answer

Given,

⇒ log₅ (x + 1) - 1 = 1 + log₅ (x - 1)

⇒ log₅ (x + 1) - log₅ (x - 1) = 1 + 1

⇒ log₅ $\dfrac{x + 1}{x - 1}$ = 2

⇒ $\dfrac{x + 1}{x - 1} = 5^2$

⇒ x + 1 = 25(x - 1)

⇒ x + 1 = 25x - 25

⇒ 25x - x = 1 + 25

⇒ 24x = 26

⇒ x = $\dfrac{26}{24} = \dfrac{13}{12} = 1\dfrac{1}{12}$ .

Hence, x = $1\dfrac{1}{12}$ .

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Mathematics

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

Logarithms

Answer

Related Questions

Given :
$\dfrac{\text{log x}}{\text{log y}} = \dfrac{3}{2}$ and log (xy) = 5; find the values of x and y.

Given log₁₀ x = 2a and log₁₀ y = $\dfrac{b}{2}$ .
(i) Write 10^a in terms of x.
(ii) Write 10^{2b + 1} in terms of y.
(iii) If log₁₀P = 3a - 2b, express P in terms of x and y.

The value of log₃ 81 is:
4
-4
$\dfrac{1}{4}$
- $\dfrac{1}{4}$

The value of log₁₆ 2 is:
4
-4
$\dfrac{1}{4}$
- $\dfrac{1}{4}$

Mathematics

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

Logarithms

Answer

Related Questions

Given :log xlog y=32\dfrac{\text{log x}}{\text{log y}} = \dfrac{3}{2}log ylog x​=23​ and log (xy) = 5; find the values of x and y.

Given log10 x = 2a and log10 y = b2\dfrac{b}{2}2b​.(i) Write 10a in terms of x.(ii) Write 102b + 1 in terms of y.(iii) If log10P = 3a - 2b, express P in terms of x and y.

The value of log3 81 is:4-414\dfrac{1}{4}41​-14\dfrac{1}{4}41​

The value of log16 2 is:4-414\dfrac{1}{4}41​-14\dfrac{1}{4}41​

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

Given :
$\dfrac{\text{log x}}{\text{log y}} = \dfrac{3}{2}$ and log (xy) = 5; find the values of x and y.

Given log₁₀ x = 2a and log₁₀ y = $\dfrac{b}{2}$ .
(i) Write 10^a in terms of x.
(ii) Write 10^{2b + 1} in terms of y.
(iii) If log₁₀P = 3a - 2b, express P in terms of x and y.

The value of log₃ 81 is:
4
-4
$\dfrac{1}{4}$
- $\dfrac{1}{4}$

The value of log₁₆ 2 is:
4
-4
$\dfrac{1}{4}$
- $\dfrac{1}{4}$