What is the solution to log5(x+30)=3
a. x=-95
b. x=-5
c. x=5
d. x=95

Keywords:

logarithmic equation, variable, logarithm, logarithm properties

For this case we have a logarithmic equation in which we must find the value of the variable x. For this we must apply properties of logarithm. By definition we have:

is equivalent to

Applying the definition, we have that: must be equivalent to:

Solving the resulting equation we have:

Clearing x:

Thus, the value of x is given by 95.

The solution of is

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

answer: c

(2, -4)

goes 7 to the

(9, 4)

easy