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

Evaluate :`1/( log_a bc + 1) + 1/(log_b ca + 1) + 1/ ( log_c ab + 1 )`

Solve for x and y ; if x > 0 and y > 0 ; log xy = log `x/y` + 2 log 2 = 2.

Evaluate: log_ba × log_c b × log_a c.

Given log₁₀x = 2a and log₁₀y = `b/2. "If" log_10^p = 3a - 2b`, express P in terms of x and y.

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

Solve the following:
log ( x + 1) + log ( x - 1) = log 11 + 2 log 3

Solve for x: `("log"81)/("log"9)` = x

State, true of false:

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

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

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