Web Reference: How to solve exponential equations with different bases. When you have an exponential equation of the form a x = b y where a and b are different bases and cannot easily be converted to the same base, the most effective strategy is to take the logarithm of both sides of the equation. If an exponential equation can be written so that both bases are the same, the equation can be solved by comparing the exponents. For example, 2x+4=8x can be written as 2x+4= (23)x. When the bases on both sides of the equation are not the same, we use logarithms to solve the exponential equations. For example, neither the bases on both sides of 5^x = 3 are the same, nor can the bases be made the same.
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