Exponential and Logarithmic Equations solve the equation. Find the exact solution if possible. otherwise, use a calculator to approximate to two decimals. e3x4=10

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Exponential and Logarithmic Equations solve the equation. Find the exact solution if possible. otherwise, use a calculator to approximate to two decimals.  e3x4=10

Luvottoq · Accepted Answer

Step 1  Law of logarithm:  Consider m to be a positive number, and m≠q1  Again consider M and N to be any real numbers with M&amp;gt;0 and N&amp;gt;0  The logarithm of power of a number is equal to the exponen times the logarithm of the number as,  logm(Mn)=NlogmM  Step 2 The  given exponential equation is,  1) e3x4=10  Take logarithm on both side of the equation (1).  2) ln⁡ e3x4=ln⁡10  Therefore, the equation (2) can be written as,  3x4ln⁡ e=ln⁡10  3x4=ln⁡10ln⁡ e  The above logarithm is a natural logarithm with base e.  The logarithm can be evaluated with a calculator as,  3x4=2.3021  3x=4(2.302)  3x=9.208  Further simplify the above equation 3x=9.208 as,  3x=9.208  x=9.2083  ≈3.06  Thus, the solution of the exponential equation e3x4=10 is x=3.06

Exponential and Logarithmic Equations solve the equation e^{3x/4}=10

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