What value of x would make the expression below equal to 8? Photo provided! 20points!

For this case, we must find the value of "x" so that the given expression is equal to 8.That is to say:[tex](\sqrt [5] {8 ^ 3}) ^ x = 8[/tex]We apply "ln" to both sides of the equation to remove the exponent variable:[tex]ln ((\sqrt [5] {8 ^ 3}) ^ x) = ln (8)\\xln (\sqrt [5] {8 ^ 3}) = ln (8)\\xln (\sqrt [5] {512}) = ln (8)[/tex]We rewrite 512 as:[tex]512 = 32 * 16 = 2 ^ 5 * 16\\xln (\sqrt [5] {2 ^ 5 * 16}) = ln (8)[/tex]By definition of power properties we have:[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]So:[tex]xln (2 \sqrt [5] {16}) = ln (8)[/tex]We clear x:[tex]x = \frac {ln (8)} {ln (2 \sqrt [5] {16})}[/tex]In decimal form, [tex]x = 1.6[/tex] periodic numberANswer:[tex]x = \frac {ln (8)} {ln (2 \sqrt [5] {16})}\\x = 1.6\ periodic\ number[/tex]