Given Log10x = 2a and Log10y = B/2. Write 102b + 1 In Terms of Y.

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

Sum

log₁₀y = `b/2`
⇒ y = 10^b/2⇒ y^{4 =}10^2b⇒ 10y⁴ = 10^2b x 10
⇒ 10^{2b + 1} = 10y⁴

shaalaa.com

More About Logarithm

Is there an error in this question or solution?

Chapter 8: Logarithms - Exercise 8 (D) [Page 111]

Chapter 8 Logarithms
Exercise 8 (D) | Q 13.2 | Page 111

If a² + b² = 23ab, show that:

log `(a + b)/5 = 1/2`(log a + log b).

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

Express log₁₀3 + 1 in terms of log₁₀x.

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

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

If log (a + 1) = log (4a - 3) - log 3; find a.

Prove that `("log"_"p" x)/("log"_"pq" x)` = 1 + log_p q

Prove that: `(1)/("log"_2 30) + (1)/("log"_3 30) + (1)/("log"_5 30)` = 1

If `"a" = "log""p"^2/"qr", "b" = "log""q"^2/"rp", "c" = "log""r"^2/"pq"`, find the value of a + b + c.