Question

how do i solve for x? thank you!

Answer 1

Answer:

$x = \frac{7}{2}$

Step-by-step explanation:

$6^{x-1} = 36 \sqrt6\\\\6^{x-1} = 6^2 \times 6^{\frac{1}{2}}\\\\6^{x-1} = 6^{2 + \frac{1}{2} }$                        $[ \ a^x \times a^ y = a^{x+ y} \ ]$

$x - 1 = 2 + \frac{1}{2}$                          $[ \ b^x = b^y => x = y \ ]$

$x = 2 + \frac{1}{2} + 1\\\\x = 3 + \frac{1}{2} \\\\x = \frac{6+ 1}{2} \\\\x = \frac{7}{2}$

Answer 2

Answer:

x = 3.5

Step-by-step explanation

       

Using the rules of exponents

$a^{m}$ × $a^{n}$ ⇔ $a^{(m+n)}$ and $\sqrt{a}$ = $a^{\frac{1}{2} }$

Then

36$\sqrt{6}$ = 6² × $6^{\frac{1}{2} }$ = $6^{(2+0.5)}$ = $6^{2.5}$

Thus

$6^{x-1}$ = $6^{2.5}$

Since the bases on both sides are equal, both 6, equate the exponents

x - 1 = 2.5 ( add 1 to both sides )

x = 3.5