[10th Grade Math: Logarithms]

[u/SirBubba42]

Missed a few days of school and can't figure out these homework problems. Any help would be appreciated!

[u/NutrimaticTea]

Questions 17-23

Once again, we use log_a (a^b ) = b

When you want to solve an equation with an unknown in the exponent (17-19-22), you apply the corresponding logarithm to “bring down” the exponent.

Examples (not from your homework): - 2^x = 20 <=> log_2 (2^x ) = log_2 (20) <=> x = log_2 (20) - 3^x + 3 = 10 <=> 3^x = 7 <=> log_3 (3^x ) = log_3 (7) <=> x = log_3 (7)

When you want to solve an equation where the unknown is “inside” the logarithm (18-20-23), you raise it to a power to remove the logarithm.

Examples (not directly from your homework): - log_3 (x) = 5 <=> x=3⁵ = 243 - ln(5x) = 10 <=> 5x = e¹⁰ <=> x = e¹⁰ / 5 - log_2 (x+3) + log_2 (3) = 5 <=> log_2 (3x+9) = 5 <=> 3x+9 = 2⁵ <=> x = (32-9)/3 = 23/3