Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Find the value of x if 3^(x+2) = 243.
3
5
4
2
3
Express both sides with the same base (base 3) and equate the powers directly without expanding.
Given exponential equation: 3^(x+2) = 243
af(x)=ag(x)тЯ╣f(x)=g(x)
Express both sides with the same base (base 3) and equate the powers directly without expanding.
Equating the base to the exponent incorrectly or miscalculating the powers of 3 (e.g., thinking 3тБ┤ = 243 instead of 3тБ╡ = 243).
Express both sides in the same base
Write the right-hand side number 243 as a power of the base 3, knowing that 35=243.
3x+2=35
Equate the exponents
Since the bases on both sides are equal, their exponents must also be equal: x+2=5.
x+2=5
Solve for x
Subtract 2 from both sides to find the value of x: x=5тИТ2=3.
x=3
A is correct because solving the equation 3x+2=243 yields x=3.
Exponential equations frequently appear in RRB JE and other competitive exams; mastering powers of small primes (2, 3, 5) saves valuable time.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants