Express Log103 + 1 in Terms of Log10x.

Express log₁₀3 + 1 in terms of log₁₀x.

Sum

log₁₀3 + 1
= log₁₀ 3 + log₁₀ 10
= log₁₀ (3 x 10)
= log₁₀30.

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Chapter 7: Logarithms - Exercise 10.2

Chapter 7 Logarithms
Exercise 10.2 | Q 9

Given log₁₀x = 2a and log₁₀y = `b/2`. Write 10^a in terms of x.

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

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

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

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

Solve the following:
`log_2x + log_4x + log_16x = (21)/(4)`

Solve for x: log (x + 5) = 1

Solve for x: `("log"125)/("log"5)` = logx

Prove that (log a)² - (log b)² = `"log"("a"/"b")."log"("ab")`

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