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Solve for x: 2^(x+3) = 32.
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Express 32 as a power of 2 (25) and equate the exponents immediately without solving the full equation.
An exponential equation 2 raised to the power (x + 3) is equal to 32.
af(x)=an⟹f(x)=n
Express 32 as a power of 2 (25) and equate the exponents immediately without solving the full equation.
Students often miscalculate 32 as 24 instead of 25, leading to an incorrect result of x=1 instead of x=2.
Express both sides with the same base
To solve for x, express 32 as a power of 2. Since 2imes2imes2imes2imes2=32, we have 32=25.
2x+3=25
Equate the exponents
Since the bases are equal (2=2), we can equate the exponents: x+3=5.
x+3=5
Solve for x
Subtract 3 from both sides of the equation to isolate x.
x=5−3=2
B is correct because the calculation x=2 satisfies the equation 2(2+3)=25=32.
This concept is essential for solving Logarithms and compound interest problems where time is the variable in the exponent.
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