When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

$\displaystyle 7^{x+5}=7^{12}$ With the same base, we can now write

$\displaystyle x+5=12$ Subtract $\displaystyle 5$ on both sides.

$\displaystyle x=7$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

$\displaystyle 12^{x+4}=12^{8}$ With the same base, we can now write

$\displaystyle x+4=8$ Subtract $\displaystyle 4$ on both sides.

$\displaystyle x=4$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

$\displaystyle 14^{x+16}=14^{-13}$ With the same base, we can now write

$\displaystyle x+16=-13$ Subtract $\displaystyle 16$ on both sides.

$\displaystyle x=-29$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

$\displaystyle 12^{2x+17}=12^{-13}$ With the same base, we can now write

$\displaystyle 2x+17=-13$ Subtract $\displaystyle 17$ on both sides.

$\displaystyle 2x=-30$ Divide $\displaystyle 2$ on both sides.

$\displaystyle x=-15$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

$\displaystyle 4=2^2$ therefore

$\displaystyle 2^{3x+8}=2^2$ With the same base, we can now write

$\displaystyle 3x+8=2$ Subtract $\displaystyle 8$ on both sides.

$\displaystyle 3x=-6$ Divide $\displaystyle 3$ on both sides.

$\displaystyle x=-2$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

$\displaystyle 27=3^3$ therefore

$\displaystyle 3^{3x-6}=3^3$ With the same base, we can now write

$\displaystyle 3x-6=3$ Add $\displaystyle 6$ on both sides.

$\displaystyle 3x=9$ Divide $\displaystyle 3$ on both sides.

$\displaystyle x=3$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

$\displaystyle 64=4^3$ therefore

$\displaystyle 4^{2x-7}=4^3$ With the same base, we can now write

$\displaystyle 2x-7=3$ Add $\displaystyle 7$ on both sides.

$\displaystyle 2x=10$ Divide $\displaystyle 2$ on both sides.

$\displaystyle x=5$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

$\displaystyle 7^0=1$ therefore

$\displaystyle 7^{4x+8}=7^0$ With the same base, we can now write

$\displaystyle 4x+8=0$ Subtract $\displaystyle 8$ on both sides.

$\displaystyle 4x=-8$ Divide $\displaystyle 4$ on both sides.

$\displaystyle x=-2$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

$\displaystyle 4=2^2, 8=2^3$ therefore

$\displaystyle (2^2)^{2x+5}=(2^3)^{x}$ Apply power rule of exponents.

$\displaystyle 2^{4x+10}=2^{3x}$ With the same base, we can now write

$\displaystyle 4x+10=3x$ Subtract $\displaystyle 4x$ on both sides.

$\displaystyle 10=-x$ Divide $\displaystyle -1$ on both sides.

$\displaystyle -10=x$

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

$\displaystyle 25=5^2, 125=5^3$ therefore

$\displaystyle (5^2)^{x+1}=(5^3)^{x+4}$ Apply power rule of exponents.

$\displaystyle 5^{2x+2}=5^{3x+12}$ With the same base, we can now write

$\displaystyle 2x+2=3x+12$ Subtract $\displaystyle 2x, 12$ on both sides.

$\displaystyle x=-10$