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 x = 1 + log 2 - log 5, y = 2 log3 and z = log a - log 5; find the value of a if x + y = 2z.

If log_√27x = 2 `(2)/(3)` , find x.

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

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

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

Solve the following:
log ₈ (x²- 1) - log ₈ (3x + 9) = 0

Solve for x: `("log"27)/("log"243)` = x

If log x = a and log y = b, write down
10^a-1 in terms of x

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