Algebra 2 help :)

Question

10^x-2=75 Solve for X

10^4x-1=35 Solve for X

8^3x=18

Please show your work and how to solve it please and thank you

Answer 1

8^3x=18

Take the common log of both sides of the equation.

3X log 8 = log 18 Use your calculator to find the logs. ( log N^x = xlogN)

3X x 0.903 = 1.26 Now rearrange and solve for X

X = 1.26/ (0.903 x3) = 0.465

The other problems are done the same way. For #2 remember to first add +1 to each side before taking the logs.

Answer 2

8^3x = 18

You know 1<3x<2 since 8^1 = 8 and 8^2= 64. Wild "educated" guess might be 3x =1.2 with x=1.2/3 = 0.4. 3x is closer to 1 than to 2. You need calculator with exponential functions or online with Desmos or a similar calculator. Solve for 3x, then divide by 3. 3x=about 1.39, divide by 3 to get about 0.46 = x. 1.39 is closer to 1 than to 2.

x=0.45 if 8^3x = 18

10^x-2 = 75. 10^2=100, 10^1= 10. 75 is closer to 100 than to 10. Wild guess is maybe x-2 = 1.7. Subtract 2. 1.7-2 =-0.3 = x

Use a calculator, x-2 = 1.875, x=1.875-2 = -0.125

x = -1/8 = -0.125 approximately

(10^4x) -1 =35

10^4x = 36

4x>1 but <2, maybe about 1.4

4x=1.557, x = 1.557/4 = about 0.39

x = 0.39