Question

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

Answer 1

The first one is the answer :)

Answer 2

Answer:

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

Step-by-step 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, $\log a^x=x\log a$

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

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

Apply change the base rule, $\frac{\log _a x}{\log _a y}=\log_y x$

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

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

Therefore, option 1 is correct.