Solve for a Variable in an Exponent
Solve for the variable:
- $4^a=16 \rightarrow 4^a=4^2 \rightarrow \mathbf{a=2}$
- $5^y=125 \rightarrow 5^y=5^3 \rightarrow \mathbf{y=3}$
- $2^x=64 \rightarrow 2^x=2^6 \rightarrow \mathbf{x=6}$
- $10^p=1 \rightarrow 10^p=10^0 \rightarrow \mathbf{p=0}$
- $25^b=5 \rightarrow 25^b=25^{\frac{1}{2}} \rightarrow \mathbf{b=\frac{1}{2}}$
- $7^{r-9}=49 \rightarrow 7^{r-9}=7^2 \rightarrow r-9=2 \rightarrow \mathbf{r=11}$
- $3^{n+5}=81 \rightarrow 3^{n+5}=3^4 \rightarrow n+5=4 \rightarrow \mathbf{n=-1}$
- $2^{2x-3}=32\rightarrow 2^{2x-3}=2^5 \rightarrow 2x-3=5 \rightarrow \mathbf{x=4}$
- $(3^x)(3^{x-1})=3^5 \rightarrow 3^{x+x-1}=3^5 \rightarrow 2x-1=5 \rightarrow \mathbf{x=3}$
- $(2^{2y})(2^{y+1})=16 \rightarrow 2^{2y+y+1}=2^4 \rightarrow 3y+1=4 \rightarrow \mathbf{y=1}$
- $(2^x)^3=8 \rightarrow 2^{3x}=2^3 \rightarrow 3x=3 \rightarrow \mathbf{x=1}$
- $(3^{3x+1})^2=27 \rightarrow 3^{6x+2}=3^3 \rightarrow 6x+2=3 \rightarrow \mathbf{x=\dfrac{1}{6}}$