MHB How to Solve These Math Equations for x?

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To solve the equation 10^(x) = 105, take the logarithm of both sides, resulting in x = log(105). For e^(x) = 100, the solution is x = ln(100). The equation 3^(2x) = 50 can be solved by taking the logarithm, yielding 2x = log(50) and thus x = 0.5 * log(50). For 0.5*e^(-x) = 0.2, rearranging gives e^(-x) = 0.4, leading to x = -ln(0.4). Lastly, ln x^(2) = 6 simplifies to x^2 = e^6, giving x = ±e^3.
Vi Nguyen
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Solve for x:

10^(x) = 105

e^(x) = 100

3^(2x) = 50

0.5*e^(-x) = 0.2

ln x^(2) = 6

5 ln 3x = 12
 
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Let's start with the first one, $10^x=105$. Where are you having difficulty?
 

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