to solve ( 49^{3x}=343^{2x + 1} ), write each side of the equation in terms of base
to solve ( 49^{3x}=343^{2x + 1} ), write each side of the equation in terms of base
Answer
Explanation:
Step1: Express 49 as a power of 7
Since (49 = 7^2), then (49^{3x}=(7^2)^{3x}). Using the power - of - a - power rule ((a^m)^n=a^{mn}), we get ((7^2)^{3x}=7^{6x}).
Step2: Express 343 as a power of 7
Since (343 = 7^3), then (343^{2x + 1}=(7^3)^{2x+1}). Using the power - of - a - power rule ((a^m)^n=a^{mn}), we get ((7^3)^{2x + 1}=7^{6x+3}).
Answer:
7