Solve for x: 125^(3x+7)=25^(5x−11)

x = 43

Step-by-step explanation:

125^(3x+7)=25^(5x−11)

Rewriting the bases as powers of 5

125 = 5^3  and 25 = 5^2

5^3 ^ (3x+7) = 5^2^(5x-11)

We know a^b^c = a^ (b*c)

5^(3 * (3x+7)) = 5^(2*(5x-11))

Distribute

5^(9x+21) = 5^(10x-22)

The bases are the same so the exponents are the same

9x+21 = 10x-22

Subtract 9x from each side

9x+21 -9x = 10x-9x-22

21 = x-22

Add 22 to each side

21+22 = x-22+22

43 = x

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

x = 3 ± √(5+y)