Question

If log, 2 =a and log,. 3 =b, then express log (5.4) in terms of 'a' and 'b'. bases are 10

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Answer 1

Given ,

log 2 = a

log 3 = b

Now ,

log 5.4

= log 54/10

= log54 - log10

= log( 9×6 ) - 1

= log ( 3×3×3×2) - 1

= log3^3 + log 2 -1

= 3log3 + log2 -1

= 3b + a -1

Answer 2

Therefore the value of $log(5.4)$ is $(a+3b-1)$

Step-by-step explanation:

Given;

$log2=a$ and $log3=b$  then $log(5.4)=?$

So,

 $log(5.4)$

$=log(\frac{54}{10})$

$=log54-log10$

$=log(2\times 3\times 3\times3)-1$   (∵ $log10=1$ )

$=log(2\times 3^{3} )-1$

$=log2+log 3^{3} -1$

$=log2+3log3-1$   (∵ $logx^{a} =alogx$ )

Plug all the values in above equation;

$=a+3b-1$

So the value of $log(5.4)$ is $(a+3b-1)$