Question

Please help me solve this

Answer 1

Answer:

x = 24

Step-by-step explanation:

using the rule of exponents

$a^{m}$ × $a^{n}$ = $a^{(m +n)}$

consider left side

$5^{\frac{x}{6} }$ × $5^{\frac{x}{2} }$

= $5^{\frac{x}{6} }$ × $5^{\frac{3x}{6} }$

= $5^{\frac{4x}{6} }$

then

$5^{\frac{4x}{6} }$ = $5^{16}$

since the bases on both sides are equal, both 5 then equate exponents

$\frac{4x}{6}$ = 16 ( multiply both sides by 6 )

4x = 96 ( divide both sides by 4 )

x = 24