Solve for a
a=-\frac{\log_{10}\left(2\right)}{4}\approx -0.075257499
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10^{1+4a}=5
Swap sides so that all variable terms are on the left hand side.
10^{4a+1}=5
Use the rules of exponents and logarithms to solve the equation.
\log(10^{4a+1})=\log(5)
Take the logarithm of both sides of the equation.
\left(4a+1\right)\log(10)=\log(5)
The logarithm of a number raised to a power is the power times the logarithm of the number.
4a=\log(5)-1
Subtract 1 from both sides of the equation.
a=\frac{\log(5)-1}{4}
Divide both sides by 4.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}