# Math Help - Solving functions equation

1. ## Solving functions equation

Need help with the following.

Thanks

2. ## Re: Solving functions equation

a) $25^{x-3}=5^x$

You can get the same base here since $25=5^2$, so that you may write:

$(5^2)^{x-3}=5^x$

$5^{2(x-3)}=5^x$

Now equate exponents, and solve for $x$.

b) $2\left(\frac{1}{2} \right)^x-\left(\frac{1}{4} \right)^x=1$

Use the substitution $u=\left(\frac{1}{2} \right)^x$ so that you may nor write:

$2u-u^2=1$

Now, solve the resulting quadratic, then back substitute for $u$.

c) $3\ln(2x+5)=9$

Divide through by 3 to get:

$\ln(2x+5)=3$

Now convert from logarithmic to exponential form and solve for $x$.

d) $e^{(x-2)^2}=2$

Convert from exponential to logarithmic form:

$(x-2)^2=\ln(2)$

Now solve for $x$ using the square root property.

e) $6^{-7x}=5$

Take the natural log of both sides to get:

$-7x\ln(6)=\ln(5)$

Now solve for $x$.