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 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 9

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

Show that : log_a m ÷ log_ab m + 1 + log _ab

If log₂(x + y) = log₃(x - y) = `log 25/log 0.2`, find the values of x and y.

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

Given x = log₁₀12 , y = log₄ 2 x log₁₀9 and z = log₁₀0.4 , find :
(i) x - y - z
(ii) 13^{x - y - z}

Evaluate : `( log _5^8 )/(( log_25 16 ) xx ( log_100 10))`

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

If `"log" x^2 - "log"sqrt(y)` = 1, express y in terms of x. Hence find y when x = 2.

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

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