Question

Which equation is equivalent to log3(x+5) = 2

Answer 1

$\\ \rm\Rrightarrow log_3(x+5)=2$

• log_a^b=c then b=a^c

$\\ \rm\Rrightarrow x+5=3^2$

$\\ \rm\Rrightarrow x+5=9$

$\\ \rm\Rrightarrow x=9-5$

$\\ \rm\Rrightarrow x=4$

Answer 2

Answer:

$3^2=x+5$

Step-by-step explanation:

Given equation:

$\log_3(x+5)=2$

Method 1

$\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b$

$\implies \log_3(x+5)=2$

$\implies 3^2=x+5$

Method 2

Make both sides of the equation the index to base 3:

$\implies \log_3(x+5)=2$

$\implies 3^{\log_3(x+5)}=3^2$

Apply the log law $a^{\log_ax}=x$ :

$\implies x+5=3^2$

Swap sides:

$\implies 3^2=x+5$

Solve for x

Although the question hasn't asked to solve for x, here is the solution:

$\implies 3^2=x+5$

$\implies 9=x+5$

$\implies x=9-5$

$\implies x=4$

Check

Substitute the found value of x into the original equation:

$x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}$