solve by expressing each power by the same base.
2^(1+2x)=32
2^(1+x) = 2^5
i do not understand what is 2,340 divisible by 90
To solve the equation 2^(1+2x) = 32 by expressing each power with the same base, we need to find a common base for both sides of the equation.
Step 1: Replace 32 with a base of 2.
Since 32 can be expressed as 2^5, we can substitute 2^5 for 32 in the equation:
2^(1+2x) = 2^5
Step 2: Apply the power rule of exponents.
According to the power rule, when two exponents with the same base are set equal to each other, the exponents must also be equal. So, we can set the exponents in this equation equal to each other:
1 + 2x = 5
Step 3: Solve for x.
To solve for x, we subtract 1 from both sides of the equation:
2x = 5 - 1
2x = 4
Finally, divide both sides of the equation by 2:
x = 4/2
x = 2
Therefore, the solution to the equation 2^(1+2x) = 32 is x = 2.