Loga M ÷ Logab M + 1 + Log Ab

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

Sum

log_a m ÷ log_ab m = =` ( log_a m )/( log_(ab) m )`

=` ( log_m ab )/( log_(m) a ) [ Qlog_b a = 1/ (log_ab ) ]`

₌ log_a ab `[ Q ( log_xx a) / (log_xx b ) = log_b a ]`

= log_aa + log_a b

= 1 + log_a b

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

Chapter 8 Logarithms
Exercise 8 (D) | Q 20 | Page 111

If log`( a - b )/2 = 1/2( log a + log b )`, Show that : a² + b² = 6ab.

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

Find x, if : log_x 625 = - 4

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

Solve for x: `("log"289)/("log"17)` = logx

Express the following in a form free from logarithm:
m log x - n log y = 2 log 5

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