Solve for X: Log 121 Log 11 = Logx

Solve for x: `("log"121)/("log"11)` = logx

Sum

`("log"121)/("log"11)` = logx

⇒ `("log"11^2)/("lo"11)` = logx

⇒ `(2"log"11)/("log"11)` = logx
= 2 = logx
⇒ 2log 10 = logx ...(since log 10 = 1)
⇒ log 10² = logx
∴ x = 10²
= 100.

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More About Logarithm

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Chapter 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 8.4

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

If log_√27x = 2 `(2)/(3)` , find x.

Solve the following:
log(x²+ 36) - 2log x = 1

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

Solve the following:
log (x + 1) + log (x - 1) = log 48

If 2 log x + 1 = log 360, find: x

If 2 log x + 1 = log 360, find: log (3 x² - 8)

If x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108, find the value of x.

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

If a b + b log a - 1 = 0, then prove that b^a.a^b = 10