Which equation has x=4 as the solution? a) ^log 4 (3x+4)=2 b) ^log 3 (2x-5)=2 c) ^log x 64=4 d) ^log x 16=4

ANSWER

EXPLANATION

Consider the equation:

When we rewrite this logarithmic equation in the exponential form, we obtain:

Note that to write a logarithmic equation in exponential form, the base of the logarithm is still the base in the exponential form.

We now simplify the RHS.

Group like terms

This implies that

Divide both sides by 3

Simplify to get;

Hence the equation that has x=4 as a solution is

Another way to do this is to substitute x=4 into each equation. The equation that is satisfied is the correct choice.

assuming you mean addition: addition and subtraction are reverse operations.

step-by-step explanation:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions