Question

If $3^7=7^x$, what is the approximate value of $x$?

• A. 0.95
• B. 1.95
• C. 2.95
• D. 3.95
• E. 4.15

Answer 1

The correct option is D 3.95

Taking log(base $10$) of both sides

we get ${\log }_{10}{3}^7={\log }_{10}{7}^x$

$\Rightarrow 7{\log }_{10}3=x{\log }_{10}7$

From the log table

$lo{g}_{10}3=0.4771$

$lo{g}_{10}7=0.8451$

So $7\times 0.4771=x\times 0.8451$

$x=\frac{7\times 0.4771}{0.8451}=\frac{3.34}{0.8451}$$=3.951$

Approximate value$=3.95$.