Question

The number of real x that satisfy the equation $\frac{8^x+{27}^x}{{12}^x+{18}^x}=\frac{7}{6}$ is

• A. $2$
• B. $3$
• C. $4$
• D. $1$

Answer 1

The correct option is D $1$

Given,

$\frac{8^x+{27}^x}{{12}^x+{18}^x}=\frac{7}{6}$

$\Rightarrow 6(8^x+{27}^x)=7({12}^x+{18}^x)$

Use trial and error method, substitute $x=1$

$6(8^1+{27}^1)=7({12}^1+{18}^1)$

$6(8+27)=7(12+18)$

$210=210$

$x=1$ satisfies the condition.

Therefore $x=1$