2 Answers

Mathias · Answer 1 · 2023-04-19T06:39:44+0000

Use the rules of exponents and logarithms to solve the equation.

$\bf{(1)/(16)*4^(x)=64 }$

Multiply both sides by 16.

$\bf{4^(x)=1024 }$

Take the logarithm of the two sides of the equation.

$\bf{log(4^(x) )=log(1024) }$

The logarithm of a number raised to a power is the power multiplied by the logarithm of the number.

$\bf{x \ log(4)=log(1024) }$

Divide the two sides by log(4).

$\bf{x=(log(1024))/(log(4)) }$

By the base change formula
$\bf{(log(a))/(log(b))=log_(b)(a). }$

$\bf{x=log_(4)(1024) }$

x = 5 ====> Answer

Please log in or register to add a comment.