Which of the following is the equation a^(2b+1)=3c-d

Question

asked Jan 13, 2018 204k views

2 Answers

Leonardo Cardoso · Answer 1 · 2018-01-17T20:14:17+0000

Answer:

Option 1 -
$\log_a (3c-d)=2b+1$

Explanation:

Given : Equation
a^(2b+1)=3c-d

To find : Which of the following is the equation ?

Solution :

Equation
a^(2b+1)=3c-d

Taking log both side,

$\log (a^(2b+1))=\log (3c-d)$

Apply logarithmic property,
$\log a^x=x\log a$

$(2b+1)\log (a)=\log (3c-d)$

$(2b+1)=(\log (3c-d))/(\log a)$

Apply change the base rule,
$(\log _a x)/(\log _a y)=\log_y x$

$(2b+1)=\log_a (3c-d)$

So, the required equation is
$\log_a (3c-d)=2b+1$

Therefore, option 1 is correct.