How do I solve log(6.5^x+25.20^x)=x+log 25?

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How do I solve  log(6.5^x+25.20^x)=x+log 25?

Bytelearn · Accepted Answer

Simplify Equation:  Step 1: Simplify the equation using properties of logarithms. We start by using the property that log(a + b) cannot be simplified directly into separate logs, but we can isolate the x on one side. log(6.5^x + 25.20^x) - log 25 = xApply Quotient Rule:  Step 2: Apply the quotient rule of logarithms. Using log(a) - log(b) = log(a/b), we rewrite the equation: log((6.5^x + 25.20^x) / 25) = xRemove Logarithm:  Step 3: Remove the logarithm by exponentiating both sides. We exponentiate both sides with base 10 to remove the logarithm: 10^(log((6.5^x + 25.20^x) / 25)) = 10^x This simplifies to: (6.5^x + 25.20^x) / 25 = 10^xClear Fraction:  Step 4: Multiply both sides by 25 to clear the fraction. 6.5^x + 25.20^x = 25 * 10^xSolve for x:  Step 5: Attempt to solve for x. This equation, 6.5^x + 25.20^x = 250^x, is complex and typically requires numerical methods or graphing to find an accurate solution. For simplicity, let's estimate by testing values of x. Testing x = 2: 6.5^2 + 25.20^2 ≈ 42.25 + 635.04 = 677.29 250^2 = 62500 (This is not equal; let's try a smaller x) Testing x = 1: 6.5^1 + 25.20^1 ≈ 6.5 + 25.2 = 31.7 250^1 = 250 (Still not equal; needs more precise calculation or a different method)

How do I solve $log(6.5^x+25.20^x)=x+log 25 ?$

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How do I solve $log(6.5^x+25.20^x)=x+log 25 ?$