the value of log9 27 log8 32 is, Logarithms, General Mathematics

Question:The value of`(log_9 27 + log_8 32)` is :

A `4` 
B `7` 
C `7/2` 
D 19/6`

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+ AnswerD

+ Explanation`let `log_9 27 = x.`

Then,`9^x = 27 ⇔ (3^2)^x`

`= 3^3`

`:. 3^2x = 3^3.`

`So, 2x = 3`

`or x = 3/2.`

let`log_8 32 = y.`

Then, `8^y = 32`

`or (2^3)^y = 2^5.`

`:.2^3y = 2^5.`

So,`3y = 5`

`or y = 5/3`.

`:. log_9 27 + log_8 32`

`= (3/2 + 5/3)`

`= 19/6.`

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